Télécom Bretagne. En habilitation conjointe avec l Université de Bretagne-Sud. Ecole Doctorale SICMA

Transcription

1 N d ordre : 2011telb0183 Sous le sceau de l Université européenne de Bretagne Télécom Bretagne En habilitation conjointe avec l Université de Bretagne-Sud Ecole Doctorale SICMA Distributed Coding Strategies for Multi-Source Cooperative Relay Networks Thèse de Doctorat Mention : Sciences et technologies de l information et la communication Présentée par Roua Youssef Département : Electronique Laboratoire : Lab-STICC Directeur de thèse : Catherine Douillard Soutenue le 5 avril 2011 Jury : Mme Maryline Hélard, Professeur, Institut National des Sciences Appliquées, Rennes (Rapporteur) M. Lars K. Rasmussen, Professeur, Royal Institute of Technology, Stockholm (Rapporteur) Mme Catherine Douillard, Professeur, Télécom Bretagne, Brest (Directeur de thèse) M. Alexandre Graell i Amat, Maître de Conférences, Chalmers University of Technology, Göteborg (Encadrant) M. Olivier Berder, Maître de Conférences, Ecole Nationale Supérieure des Sciences Appliquées et de Technologie, Lannion (Examinateur) M. Chistrian Roland, Maître de Conférences, Université de Bretagne Sud, Lorient (Examinateur)

2 Dedication To my parents i

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4 Acknowledgment I wish to express my sincere gratitude to my advisor Doctor Alexandre Graell i Amat. I would like to thank him for his supervision, advice and guidance from the very early stage of this research. I would like to thank Professor Catherine Douillard and I appreciate her effort on reading my thesis and giving comments. I also would like to thank Professor Ramesh Pyndiah for the fruitful discussions we had. I also wish to thank the committee members, especially Professor Maryline Hélard and Professor Lars K. Rasmussen, for reading and accepting my thesis. Furthermore, I gratefully acknowledge the members of Pracom for providing financial support for the three years of my thesis. I am also thankful to all the members of the Electronics Department at Telecom Bretagne. I would also thank all my friends I have met in Brest and with whom I have spent an unforgettable time. Finally, I thank my family in Lebanon for their continuous support through all ups and downs of my thesis years. iii

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6 Abstract Cooperative communication in wireless networks has recently been introduced as a new method to increase the throughput, the reliability and the robustness of the wireless system. The basic idea of cooperative communications is that all nodes in a network may help each other to transmit information to a destination. This thesis addresses cooperative coding schemes for wireless networks with relays. The main part of this thesis investigates the design of distributed serially concatenated codes for relay networks. In this work, scenarios where multiple sources communicate with a destination with the help of a relay are considered. The main contribution of this thesis is the construction of a powerful code distributed over all the nodes in the network. Time allocation between the sources and the relay is also addressed in order to improve the performance of the network. The proposed coding scheme achieves very low error rates and offers significant performance gains with respect to non-cooperation, even for a very large number of sources. Furthermore, it provides a high flexibility in terms of code rate, number of sources, overall system rate and error protection. The proposed distributed coding scheme fits well for applications such as sensor networks where each sensor deals with a small amount of information. v

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8 Résumé Le concept des communications coopératives pour les réseaux sans fil a été récemment introduit dans le but d augmenter le débit et d améliorer la qualité de transmission et la robustesse de ces réseaux. Le principe sous-jacent repose sur l idée de base que plusieurs nœuds dans un réseau peuvent s entraider pour transmettre l information à la destination. Cette thèse traite des schémas de codage coopératifs pour les réseaux sans fil avec relais. Dans ce travail, nous étudions la conception des codes distribués concaténés en série pour les réseaux à relais. Des scénarios où plusieurs sources communiquent avec une destination à l aide d un relais sont considérés. La contribution majeure de la thèse est la construction d un code puissant distribué sur l ensemble des nœuds du réseau. En outre, l optimisation de l allocation temporelle entre les sources et le relais est étudiée afin d améliorer les performances globales du système. Le schéma proposé permet d atteindre des taux d erreurs très faibles et montre des gains de codage et de diversité importants par rapport aux systèmes non coopératifs. Il offre de plus une grande flexibilité en termes de rendement de codage, du nombre d utilisateurs et du niveau de protection des erreurs. Un scénario typique pour le schéma de codage proposé est le réseau de capteurs sans fil où chacun des nœuds traite une petite quantité d information. vii

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10 Résumé de la thèse Chapitre 1: Introduction Les communications sans fil ont connu un essor particulier et sont devenues vitales dans notre vie quotidienne. Le défit à relever par la communauté scientifique était toujours de concevoir des systèmes de communication assurant une transmission fiable, une meilleure efficacité spectrale et qui sont capables de combattre l évanouissement. Un moyen pour relever ce défit est d exploiter la diversité temporelle, fréquentielle ou spatiale. Une des techniques les plus connues qui exploitent la diversité consiste à utiliser plusieurs antennes à l émission. Cependant, plusieurs dispositifs de communication sans fil ont des contraintes de complexité et de taille limitée et de ce fait il n est pas toujours possible d employer plusieurs antennes à l émission. Un nouveau concept connu sous le nom de la communication coopérative offre une méthode alternative pour assurer une meilleure diversité ainsi qu une transmission plus fiable et plus robuste. L idée clé de la communication coopérative est que plusieurs nœuds dans un réseau s entraident les uns les autres pour transmettre leurs informations à la destination en exploitant la nature du canal de diffusion sans fil. Les communications coopératives permettent ainsi de partager plusieurs antennes répartis sur différents nœuds. Les discussions sur les communications coopératives remontent au célèbre papier de Van der Meulen [vdm71] sur le canal à relais qui consiste en une source, un relais et une destination. Des études théoriques ont été menées par Cover et El Gamal [CG79] et les bornes supérieures et inférieures de la capacité ont été dérivées. Afin de récolter les gains prédits par la théorie de l information, des schémas coopératifs ont été récemment proposés dans [VZ03, ZD05]. Dans [VZ03], une nouvelle technique de codage appelée turbo code distribué a été proposée pour le canal à relais. Dans le schéma proposé, la source émet au relais et à la destination à la fois. Le relais décode, entrelace et recode le message avant de l émettre. La destination reçoit deux versions codées du message original et les décode conjointement par un algorithme de décodage itératif. Des gains de diversité ainsi que de codage sont obtenus par cette technique. Plus récemment, des schémas de codage de canal et de réseau conjoints ont été proposés dans [HSOB05, YK07] pour le canal à relais à accès multiple. Dans [HSOB05], deux sources émettent à la destination et au relais, celui-ci émet à son tour une combinaison (simple OU ix

11 x RÉSUMÉ DE LA THÈSE exclusif) des messages reçus des deux sources. L idée de base est d avoir des nœuds très simples, avec de simples opérations de codage, et de construire un code puissant distribué sur les différents nœuds dans le réseau. Ce concept peut évidemment être étendu à différents nombres de nœuds. Cependant, la plupart des travaux qui ont traité les communications coopératives se limitent à seulement deux sources et l extension à de multiples sources en gardant de bonne performance n est pas simple. Dans cette thèse, nous nous intéressons aux réseaux multiutilisateurs. Le but est de proposer une stratégie de codage flexible qui, à la différence des approches classiques qui optimisent la communication sur le canal point-à-point, considère le réseau tout entier. Dans ce travail, nous proposons un code distribué concaténé en série pour un réseau multi-source sans fil à relais. Les différentes sources communiquent avec une seule destination aidées par un relais commun qui utilise la technique decode-and-forward. Le réseau global est vu comme un code concaténé en série qui s avère être très puissant, même pour des blocs de taille courte et un grand nombre de sources. Nous évaluons et analysons les performances de notre système et nous les comparons aux systèmes non-coopératifs. Dans la suite, le contenu de chaque chapitre est décrit séparément.

12 RÉSUMÉ DE LA THÈSE xi Chapitre 2: Contexte et Notions de base Ce chapitre résume les concepts basiques de la théorie de l information et du codage de canal utilisés dans les chapitres suivants. Les codes concaténés en parallèle et en série, ainsi que leur décodage et les outils utilisés pour analyser ce dernier sont présentés. Ensuite, ce chapitre est complété par la présentation des différentes techniques utilisées dans les communications multiutilisateurs. En outre, nous décrivons brièvement le codage de réseau récemment considéré conjointement au codage de canal pour les réseaux sans fil avec relais.

13 xii RÉSUMÉ DE LA THÈSE Chapitre 3: Les Communications Coopératives pour les Réseaux sans Fil Le chapitre 3 introduit les communications coopératives et les différents aspects de coopération. Dans ce chapitre, différentes stratégies de communication pour les réseaux à relais sans fil sont présentées. Trois topologies de réseaux coopératifs sont considérées: le canal à relais, le canal à relais à accès-multiple et la topologie de coopération entre deux sources. Nous commençons par considérer le modèle de coopération le plus simple qui est le canal à relais illustré dans la figure 1. Des schémas de codage distribué pour ce canal sont présentés. Ensuite, nous considérons un cas plus général, le canal à relais à accès-multiple de la figure 2 et nous présentons des schémas de codage de réseau et de canal conjoint pour ce type de canal. Dans ce chapitre, nous nous restreignons à deux sources seulement. Enfin, nous considérons une topologie où deux sources communiquent entre eux comme illustré dans la figure 3 et chaque source joue le rôle du relais pour son partenaire. Figure 1 Le canal à relais: une source, un relais et une destination. r d Figure 2 Le canal à relais à accès-multiple: source s 1 et s 2 émettent à une destination en présence d un relais. Figure 3 Chaque source joue le rôle de relais pour son partenaire.

14 RÉSUMÉ DE LA THÈSE xiii Chapitre 4: Codes Concaténés Distribués pour les Réseaux Coopératifs sans Fil Dans ce chapitre, nous considérons un scénario général où plusieurs sources communiquent avec une destination en présence d un relais. Le scénario considéré est illustré dans la figure 4. Un scénario typique pour le schéma de codage proposé est le réseau de capteurs sans fil où plusieurs nœuds traitent une petite quantité d information et communiquent avec une destination aidés par un nœud central, qui possède moins de restrictions sur les ressources que les sources. Nous proposons un schéma de codage de la famille turbo pour un scénario multiutilisateur où plusieurs sources émettent à une destination aidées par un relais commun qui utilise la stratégie decode-and-forward et qui opère en mode half-duplex. Un scenario orthogonal est considéré dans ce chapitre. L orthogonalité est obtenue par la technique d accès multiple à répartition dans le temps (TDMA). Le relais décode les informations de toutes les sources, les combine et les recode pour générer une redondance additionnelle. Cette redondance est ensuite transmise à la destination. Deux stratégies de codage au relais sont proposées. La quantité d information émise par le relais peut être ajustée simplement selon les performances, l efficacité spectrale et/ou la puissance souhaitées. r d Figure 4 Un réseau à relais sans fil: plusieurs sources transmettent à une seule destination aidées par un relais commun. A la destination, le décodage de l information de toutes les sources est effectué conjointement d une façon itérative exploitant la redondance fournie par le relais. Le réseau de communication global peut être vu comme un code concaténé en série où le codeur externe groupe les codeurs des sources et le code interne est celui du relais. En conséquence, le récepteur peut décoder l information de toutes les sources en utilisant une stratégie de décodage semblable à celle des codes concaténés en série classiques. Dans ce chapitre, nous présentons la stratégie que nous avons adoptée pour optimiser les performances de notre système en termes de error floor et de convergence. Les polynômes des codeurs ont été choisis de façon à améliorer le floor et ensuite les autres paramètres, i.e., les rendements des codes externes et internes, sont optimisés selon d autres paramètres comme la maximisation du rendement atteignable. Des

15 xiv RÉSUMÉ DE LA THÈSE études théoriques de notre système sont menées en termes de rendement atteignable et probabilité de coupure. En outre, nous étudions l allocation de temps entre les sources et le relais et nous dérivons une expression sous forme close de l allocation de temps optimale qui maximise le rendement atteignable. Les diagrammes EXIT sont ensuite utilisés pour analyser le comportement de notre système en convergence et aussi comme un outil d optimisation des paramètres du code distribué concaténé en série. Le code concaténé en série proposé atteint de faibles taux d erreur pour un grand nombre de sources et de blocs de petite taille et présente un gain significatif par rapport aux systèmes non-coopératifs. Dans notre approche, même pour les blocs de taille courte (par exemple 96 bits), le code distribué global s avère être très puissant et atteint de faible taux d erreurs pour différents nombres de sources (q 2). Cela est dû aux deux faits: Tout d abord, les informations de toutes les sources sont combinées et entrelacées par un même entrelaceur avant le codage au relais. Cela permet d atteindre un double gain, le gain de diversité et le gain d entrelacement. Ensuite, la présence de plusieurs sources permet de construire un code de taille longue et par conséquent un code global très robuste. La stratégie de codage proposée est flexible, en d autres termes, le système conçu est capable de s adapter d une manière très simple à différent nombre de sources ainsi qu aux différents rendements. En outre, la quantité d information émise par le relais est contrôlée selon les performances souhaitées par de simples opérations au relais. En plus de ces avantages, notre système présente la possibilité d être étendu d une façon simple aux scénarios avec plusieurs relais et plusieurs destinations.

16 RÉSUMÉ DE LA THÈSE xv Chapitre 5: Scénarios Multiutilisateurs avec Interférence Due à l Accès Multiple Pour des applications sensibles au délai (e.g., les transmissions des vidéos et des paroles), les scénarios non-orthogonaux où plusieurs sources transmettent dans la même bande de fréquence ou dans le même temps sont plus pratiques. Motivés par le fait que beaucoup de travaux ont été menés pour les réseaux à relais sous l hypothèse des canaux orthogonaux tandis que les scénarios non-orthogonaux ont été peu traités, nous considérons dans ce chapitre des scénarios avec interférence due à l accès multiple. Nous proposons un schéma de codage distribué adapté aux scénarios nonorthogonaux où les différentes sources transmettent simultanément. Pour la détection multiutilisateur, la technique IDMA (interleave-division multiple-access) est utilisée. Le choix de cette technique est justifié par la faible complexité de son algorithme de détection qui augmente linéairement avec le nombre de sources. Dans un premier temps, nous considérons un relais half-duplex, i.e., le temps d émission est divisé en deux unités; la première unité de temps est dédiée aux sources et la deuxième au relais. Un émetteur IDMA est utilisé à chaque source et un récepteur IDMA est utilisé au relais et à la destination. Le signal émis par le relais est reçu séparément. Des analyses théoriques en termes de rendement atteignable et optimisation de l allocation de temps entre les sources et le relais sont menées. Les résultats de simulation montrent un gain de codage important par rapport à un système IDMA non-coopératif. Dans un deuxième temps, nous considérons un scénario où le relais est full-duplex, i.e., les sources et le relais émettent simultanément. Nous adaptons la stratégie de codage à ce scenario. Le système proposé présente un gain par rapport au cas noncoopératif, par contre il est moins performant que celui du scénario avec un relais half-duplex.

17 xvi RÉSUMÉ DE LA THÈSE Chapitre 6: Conclusions et Perspectives Cette thèse traite les schémas de codage coopératifs pour les réseaux sans fil avec relais. La contribution majeure de cette thèse est dans la conception des codes distribués concaténés en série pour les réseaux à relais. Dans ce travail, des scénarios où plusieurs sources communiquent avec une destination à l aide d un relais sont considérés. Le but est de construire un code puissant distribué sur tous les nœuds du réseau. En outre, l allocation de temps entre les sources et le relais est traitée afin d améliorer les performances du système. Le schéma proposé permet d atteindre des taux d erreurs très faibles et offre des gains importants par rapport aux systèmes non coopératifs. En plus, il offre une grande flexibilité en termes de rendement de code, nombre d utilisateurs et niveau de protection d erreur. Une application potentielle du schéma de codage proposé est le réseau de capteurs où chaque capteur traite une information de taille petite. Pour conclure, nous donnons quelques perspectives qui apparaissent à l issue de notre travail et qui permettent de l étendre: Dans notre travail, nous avons considéré un cas symétrique où les sources émettent avec le même rendement. Un cas non-symétrique peut aussi être considéré. En outre, l optimisation de l allocation de puissance peut être traitée pour un tel cas. L allocation de puissance pour les systèmes à relais est considérée dans [HMZ05, YAJ06]. Pour des transmissions non fiables entre les sources et le relais, les techniques ARQ (automatic repeat request) peuvent être adoptées afin de renforcer les liens source-relais et source-destination. Les protocoles ARQ pour les schémas à relais sont traités dans [YZQ06, YZQ07, FLGB10]. Une autre solution possible pour les transmissions non fiables au relais est de changer le protocole decode-and-forward au relais, et de considérer le protocole compress-and-forward par exemple. Différents travaux ont proposé des techniques de compression pour le canal à relais [RJ06] et le canal à relais à accès-multiple avec deux sources [ZKBW08] et peuvent être étendus à notre système. Dans notre étude, nous avons considéré un réseau avec des sources indépendantes. Une piste intéressante à explorer sera de considérer des sources corrélées. Le canal à relais à accès-multiple avec des sources corrélées est traité dans [SCKGG07].

18 Contents Dedication Acknowledgment Abstract Résumé Résumé de la thèse Table of contents List of figures List of tables Acronyms i iii v vii ix xvi xxi xxvii xxix 1 Introduction 1 2 Background and Basic Principles Channel Model for Wireless Communications Noise Path-Loss Propagation Fading Channel Model Information Theoretic Limits Entropy and Mutual Information Channel Capacity Outage Probability Channel Coding Convolutional Codes Parallel Concatenated Codes xvii

19 xviii CONTENTS Serially Concatenated Codes FlexiCode Iterative Decoding of Concatenated Codes The Logarithm Likelihood Ratio Iterative Decoding of a PCC Iterative Decoding of an SCC Iterative Decoding of a FlexiCode Extrinsic Information Transfer Charts Multiuser Transmission Frequency Division Multiple Access Time Division Multiple Access Coded Division Multiple Access Interleaved Division Multiple Access IDMA transmitter IDMA receiver Network Coding Conclusions Cooperative Communications in Wireless Networks The Relay Channel Channel Model Achievable Rates of the Relay Channel Achievable Rate in the case of Equal Time Allocation Achievable Rate in the case of Optimal Time Allocation Achievable Rate and Relay Position Outage Probability Distributed Codes for the Relay Channel Distributed Parallel Concatenated Codes Distributed Serially Concatenated Codes The Multiple-Access Relay Channel Achievable Rates for the MARC Achievable Rate with Equal Time Allocation Achievable Rate with Optimal Time Allocation Outage Probability for the MARC Joint Channel-Network Coding for the Multiple-Access Relay Channel Encoding Scheme for Reliable Source-to-Relay Transmission Noisy Source-to-Relay Channel How to Process the Information at the Relay? Coded Cooperation in a Two-User Scenario

20 CONTENTS xix Two-User Cooperation Network Coding in Orthogonal Two-User Cooperative Scenario Network Coding in Non-Orthogonal Two-User Cooperative Scenario Conclusions Distributed Turbo-Like Codes for Multiuser Cooperative Scenarios System Description System Model Channel Model Encoding Strategies at the Relay Encoding Strategy A Encoding Strategy B The Relay Network Regarded as a Serially Concatenated Code Decoding of the Distributed Serially Concatenated Code Decoding for Strategy A Decoding for Strategy B A Particular Case: The Overall Network Performing as a Parallel Concatenated Code Code Optimization Information Theoretic Limits Achievable Rates Achievable Rates with Equal Time Allocation Achievable Rates with Optimal Time Allocation Outage Behavior over the q-marc EXIT Chart Analysis EXIT Charts with Equal Time Allocation EXIT Charts with Optimal Time Allocation Simulation Results Simulation Parameters and Reference Systems Results for Equal Time Allocation Results for Optimal Time Allocation Results for Equal Coding Rate Results over Block Fading Channels Distributed Serially Concatenated Codes for Unreliable Source-to-Relay Transmission Conclusions Multi-User Scenario with Multiple-Access Interference Distributed Serially Concatenated Codes for Half-Duplex Relay with Multiple-Access Interference

21 xx CONTENTS System Description System Model Channel Model Multiuser Detection at the Relay Encoding Strategies at the Relay Decoding at the destination Information Theoretic Limits Channel Capacity of Multiple-Access Channel with q Layers Achievable Rates over the MARC Simulation Results Full Simultaneous Multiple-Access System System Description Decoding at the destination Simulation Results Comparison of the Two Scenarios Conclusions Conclusions and Perspectives 115

22 List of Figures 1 Le canal à relais: une source, un relais et une destination xii 2 Le canal à relais à accès-multiple: source s 1 et s 2 émettent à une destination en présence d un relais Chaque source joue le rôle de relais pour son partenaire xii 4 Un réseau à relais sans fil: plusieurs sources transmettent à une seule destination aidées par un relais commun xiii 1.1 Hierarchical communication structure: multiple sources communicate with an access point via multiple relays Block diagram of a digital communication system Channel capacities in bits per second for Gaussian input variables and BPSK modulation over AWGN channel Spectral efficiencies in bits per second per Hertz for Gaussian input variables and BPSK modulation over AWGN channel Outage probability for Gaussian distributed input variables and BPSK modulation for a rate R = 1/2 over Rayleigh block fading channel Rate 1/2 recursive systematic convolutional code with memory ν = Block diagram of a PCC General block diagram of an SCC Block diagram of the SCC introduced in [GMV05, GMV09] Flexicode encoder block diagram Typical behavior of turbo-like codes Iterative decoding of a PCC BER curve of A PCC over an AWGN channel, R = 1/2, k = 1504 bits, 10 iterations Iterative decoding of an SCC BER curves comparison between an SCC and a PCC over AWGN channel, R = 1/2, k = 1504 bits, 10 iterations. The PCC suffers from an error floor between BER 10 6 and Iterative decoding of a FlexiCode xxi xii

23 xxii LIST OF FIGURES 2.16 FER performance after 10 iterations for R = 1/2, 2/3 and 5/6 with k = 1504 bits. An AWGN channel is assumed with BPSK modulation EXIT Chart of the SCC: rate-1/2 outer convolutional code of generator polynomials (07,05) and rate-1 inner convolutional code of generator polynomials (03,02) Multiplexing principle of FDMA Multiplexing principle of TDMA Multiplexing principle of CDMA Block diagram of an IDMA transmitter Block diagram of an IDMA receiver The butterfly network with routing: a multicast rate of 1.5 bits per unit time is achieved The butterfly network with network coding: a multicast rate of 2 bits per unit time is achieved The relay channel: a three terminal channel Achievable rate over the relay channel with equal time allocation, d sr /d sd = 1/4 and Gaussian input variables The achievable rate plotted as a function of γ sd and the relay position d sr /d sd : the peak value is reached for d sr /d sd = 1/2 for low SNRs. For high SNRs, flatter curves are observed. BPSK modulation is considered Outage probability for BPSK modulation for a rate R = 1/3 over Rayleigh block fading channel Block diagram of the DPCC Simulation results over AWGN channel ; d sr /d sd = 1/4; k = 1504 bits Simulation results over AWGN channel ; d sr /d sd = 3/4; k = 1504 bits. BER performance comparison between the classic DF and the use of F p at the decoders Block diagram of the DSCC user MARC: sources s 1 and s 2 transmit to a single destination with the help of a relay Achievable sum rate for the 2-users MARC for both equal and optimal time allocation over AWGN channel and Gaussian input variables Outage probabilty for a rate R = 1/3 with BPSK modulation over the 2- user MARC and for the non-cooperative transmission. AWGN channels are considered Block diagram of the joint network/channel coding scheme proposed in [HD06] Iterative decoding at the destination Block diagram of the joint network coding scheme for noisy relay proposed in [YK07]

24 LIST OF FIGURES xxiii 3.15 Iterative decoding at the destination BER curves over AWGN channel for both soft case(red curves) and hard case (blue curves). γsr b = 5 db and different values of γrd b are considered (γrd b = 10, 5,0,5,10 db) BER curves over AWGN channel for both soft case(red curves) and hard case (blue curves). γsr b = 0 db and different values of γrd b are considered (γrd b = 0,5,10 db) Two-user cooperation: Each source acts as a relay for its partner The four possible cases of cooperation depending whether each source decodes successfully or not its partner information FERcurvesoverRayleighblockfadingchannel;k = 500bits;R eff = 1/3; 10 iterations BER curve over AWGN channel; k = 4096 bits, 15 iterations BER curve over AWGN channel; k = 500 bits, 10 iterations A wireless relay network: multiple sources transmit to a single destination with the help of a common relay Block diagram of the proposed coding scheme. The relay processes information using strategy A Block diagram of the proposed coding scheme. The relay processes information using strategy B Equivalent representation of the wireless relay network of Figure 4.2 and Figure Joint iterative decoding when the relay operates using strategy A. We enumerate the decoding steps (scheduling) from (1) to (5) Joint iterative decoding when the relay operates using strategy B. We enumerate the decoding steps (scheduling) from (1) to (3) Achievable sum rate as a function of γ sd and the relay position: At low SNRs the peak is reached for d= Outage probability over the MARC for q = 4,8 and 20 for an overall rate R eff = q (solid curves) and outage probability for the non 2(q+1) cooperative system (dashed curves) Another equivalent representation of the distributed SCC of Figures 4.2 and EXIT chart of the proposed distributed turbo-like code, strategy B, for q = 2 and q = 4 users. Fast fading Rayleigh channel. d sr = (1/4)d sd and d rd = (3/4)d sd. R eff = q. The convergence threshold for q = 2 is 2(q+1) γsd b = 0.77 db and for q = 4 is γb sd = 1.57 db EXIT chart of the proposed distributed turbo-like code, strategy A, for q = 8 and q = 20 users. Fast fading Rayleigh channel. d sr = (1/4)d sd and d rd = (3/4)d sd. R eff = q. The convergence threshold for q = 8 2(q+1) is γsd b = 2.32 db and for q = 20 is γb sd = 3.52 db

25 xxiv LIST OF FIGURES 4.12 EXIT chart of the proposed distributed turbo-like code, strategy B, for q = 4 users with optimal time allocation. Fast fading Rayleigh channel. R eff = q. The convergence threshold for q = 4 is 2(q+1) γb sd = 0.35 db FER curves for the distributed SCC using strategy A (filled markers) and B (empty markers) for q = 2,8,20 and 50 sources and equal time allocation over Rayleigh fast fading channel. R i = R s = 1/2, R eff = q.d 2(1+q) sr = (1/4)d sd and d rd = (3/4)d sd. k i = k = 96 bits, 15 iterations. CC=convolutional code and TC=turbo code FER curves for the distributed SCC using strategy A (filled markers) and B (empty markers) for q = 4,16,30 and 100 sources and equal time allocation over Rayleigh fast fading channel. R i = R s = 1/2, R eff = q 2(1+q). d sr = (1/4)d sd and d rd = (3/4)d sd. k i = k = 96 bits, 15 iterations. CC=convolutional code and TC=turbo code FER curves of the distributed SCC for two settings: d sr = (1/4)d sd and d sr = (1/2)d sd. R eff = q, k 2(1+q) i = k = 96 bits, 15 iterations, fast fading channel. For d sr = (1/2)d sd, an error floor is observed between FER 10 4 and FER curves of the distributed SCC with respect to the distributed PCC, R eff = q. k 2(1+q) i = k = 96 bits, 15 iterations, fast fading channel. The distributed PCC suffers from an error floor between FER 10 4 and FER curves for the distributed SCC using strategy B for q = 20 and 100 sources over Rayleigh fast fading channel, for optimal (illed markers) and equal (empty markers) time allocation. R eff = q. k 2(1+q) i = k = 96 bits, 15 iterations FER curves for the distributed SCC using strategy B for q = 2,4,20 and 100 sources over Rayleigh fast fading channel for a fixed rate R eff = 1/3 and equal time allocation. k i = k = 96 bits, 15 iterations FER curves for the distributed SCC using strategy B for q = 2,4,20 and 100 sources over Rayleigh fast fading channel for a fixed rate R eff = 1/3 and optimal time allocation. k i = k = 96 bits, 15 iterations CFER curves for the distributed SCC using strategy A (solid line, filled markers) and CFER curves for the non cooperation system (solid line, empty markers) for q = 2,4 and 20 sources over Rayleigh block fading channel. k i = k = 96 bits, 15 iterations. The outage probability curves are also reported (dashed lines) FER curves for the distributed SCC using strategy A for q = 20 sources over Rayleigh fast fading channel, d sr = (3/4)d sd. R eff = q. k 2(1+q) i = k = 96 bits, 15 iterations. The solid curves correspond to the system with F pi used at the decoders and the dashed curves to classic decoding... 91

26 LIST OF FIGURES xxv 5.1 The transmission time is divided into two slots: one time slot is allocated for the q sources transmission and the relay transmits in the second time slot IDMA receiver at the destination node Multiple-access channel with q layers Channel capacity of a binary multiple-access AWGN channel with q layers assuming equal transmission rates per layer as done in IDMA and perfect successive interference cancellation FER curves, non-cooperation scheme (empty markers), cooperation scheme with strategy A (filled markers), with q = 2,4,8 sources, over fast fading channel. R i = R s = 1/2, R eff = q. k 4m i = k = 96 bits, 30 iterations FER curves, non-cooperation scheme (empty markers), cooperation scheme with strategy B (filled markers), with q = 12 and 16 sources, over fast fading channel. R i = R s = 1/2, R eff = q. k 4m i = k = 96 bits, 30 iterations Transmission time allocation for simultaneous multiple-access IDMA transmitter at the relay: After encoding using strategy A or B, a spreading code followed by an interleaver is used at the relay IDMA receiver at the destination for full simultaneous multiple-access FER curves, non-cooperation scheme (empty markers), cooperation scheme (filled markers), with q = 2 and 4 sources, over fast fading channel. k i = k = 96 bits, 30 iterations FER curves, non-cooperation scheme (empty markers), cooperation scheme (filled markers), with q = 8, 12 and 16 sources, over fast fading channel. k i = k = 96 bits, 30 iterations FER curves comparison: two-slot scenario (dashed curves) and full simultaneous multiple-access (solid curves)

27

28 List of Tables 3.1 Equivalent signal to noise ratio γeq b Transmission time for two time slots (four successive half slots) Transmission time for two time slots Minimum γsd b that achieves a rate of R eff = q when equal time is 2(q+1) allocated for the sources and the relay Minimum γsd b that achieves a rate of R eff = q and optimal time 2(q+1) allocation parameters for the distributed serially concatenated schemes for different number of users Convergence thresholds for the distributed serially concatenated schemes for different number of users d sr /d sd = 1/ Convergence thresholds for the distributed serially concatenated schemes for different number of users for d sr /d sd = 1/ Convergence thresholds for the distributed serially concatenated schemes for different number of users with optimal time allocation Minimum values of γsd b achieved over fast fading channel with equal time allocation Minimum values of γsd b achieved over fast fading channel with optimal time allocation xxvii

29

30 Acronyms AF Amplify and Forward APP A Posteriori Probability ARQ Automatic Repeat request AWGN Additive White Gaussian Noise BCJR Bahl, Cocke, Jelinek and Raviv BER Bit Error Rate BPSK Binary Phase Shift Keying CDMA Coded Division Multiple Access CF Compress and Forward CFER Common Frame Error Rate DF Decode and Forward DPCC Distributed Parallel Concatenated Code DSCC Distributed Serially Concatenated Code DVB Digital Video Broadcasting ESE Elementary Signal Estimator EXIT EXtrinsic Information Transfer FER Frame Error Rate FDMA Frequency Division Multiple Access GSM Global System for Mobile Communications IDMA Interleaved Division Multiple Access xxix

31 xxx ACRONYMS LLR Log Likelihood Ratio MAC Multiple Access Channel MAP Maximum A Posteriori MARC Multiple Access Relay Channel MIMO Multiple-Input Multiple-Output MRC Maximum Ratio Combining PCC Parallel Concatenated Code pdf probability density function SCC Serially Concatenated Code SISO Soft Input Soft Output SNR Signal to Noise Ratio SOVA Soft Output Viterbi Algorithm SPC Single Parity Check TDMA Time Division Multiple Access UMTS Universal Mobile Telecommunications System WiMAX Worldwide Interoperability for Microwave Access

32 CHAPTER 1 Introduction The birth of wireless communications dates back to 1897, when Marconi established in his pioneering work the first radio link between a land-based station and a tugboat. Since then, wireless communication systems have witnessed a tremendous evolution and have become vital in our everyday life. For instance, the number of worldwide mobile subscribers has increased from a few million in 1990 to more than 4 billion in 2010 [Por09]. With this growth of wireless devices and applications, the challenge for the wireless research community has always been to design communication systems which continue to achieve reliable transmission, high spectral and power efficiency and are able to mitigate the fading and interference effects. A way to overcome this challenge is by exploiting diversity in time, in frequency or space. A well-known technique which exploits diversity consists in employing more than one antenna at the transmitter. However, many wireless devices have limited size or hardware complexity, therefore it is not always possible to employ multiple antennas at the device. A new concept called cooperative communications offers an alternative method to achieve increasing diversity, robustness and reliable transmission. The key idea of cooperative communications is that, exploiting the inherent broadcast nature of the wireless channel, several nodes help each other to transmit information to the destination. While a single antenna is employed at each node, cooperative communications allow to share several antennas distributed over different nodes. Cooperative communications bring higher data throughput, spectral and power efficiency, and reliability. User cooperation was first discussed in the pioneering paper by van der Meulen on the relay channel [vdm71], a three-terminal network which consists of a source, a relay and a destination. The relay channel was further investigated by Cover and El 1

33 2 CHAPTER 1. INTRODUCTION Gamal in [CG79], where upper and lower bounds to the capacity were derived, and two basic coding strategies were proposed: decode-and-forward, and compress-and-forward, where the relay decodes and compresses, respectively, the source information prior to forwarding. In order to harvest the gains predicted by information theory, practical cooperation schemes have been recently proposed in [VZ03, ZD05]. In [VZ03], a novel coding technique for the relay channel called distributed turbo code was proposed. In the proposed scheme, the source broadcasts to both the relay and the destination. The relay decodes, interleaves and re-encodes the message prior to forwarding. The destination receives two encoded copies of the original message and jointly decodes them by an iterative decoding algorithm. The proposed technique achieves a combined diversity and coding gain. More recently, joint network and channel coding schemes have been proposed in [HSOB05, YK07] for a multiple-access relay channel. In [HSOB05], two sources transmit to both the destination and the relay, which forwards a combination (a simple XOR) of the received messages from both sources. The main idea is to have very simple nodes, with simple encoding operations, and construct a powerful code distributed over the network nodes. This concept can obviouslybeextendedtoanynumberofnodes.however,inmostoftheworkoncooperative communications the number of sources is limited to at most two, and the extension to multiple sources with good performance is not straightforward. In this thesis, we are interested in networks with multiple sources. The aim is at proposing a flexible encoding strategy which does not consist on the classical approach of individually optimizing communication over point-to-point channels but in considering the overall network. An important application of such networks is wireless sensor networks. A wireless sensor network is generally built as a hierarchical structure [SKM04b]. A hierarchical wireless sensor network consists of a cluster of sensors, intermediate relays which have less stringent restrictions on resources than the sensors and serve exclusively as forwarders, and a central server or access point. Figure 1.1 depicts this hierarchical communication structure. Such a network with a single forwarding node, i.e., a single relay, can be modeled as a multiple-access relay channel (MARC) which is a multisource extension of the well-known single-user relay channel. In this work, we propose distributed serially concatenated coding schemes for a multi-source wireless relay network where multiple sources transmit to a single destination with the help of a common relay, which uses the decode-and-forward strategy. The overall network is regarded as a serially concatenated code which turns out to be very powerful even for short block length and large number of sources. We evaluate and analyze the performance of our system and compare it with respect to non-cooperation.

34 3 Sensors Relays Figure 1.1 Hierarchical communication structure: multiple sources communicate with an access point via multiple relays. Outline and Contributions This thesis is organized in the typical-order way, where the basic concepts are presented in the beginning and the new contributions in the following chapters. The contents of the individual chapters are outlined in the following. Chapter 2 reviews some basic concepts about information theory and channel coding which are required for the next chapters. We provide an overview of concatenated codes, their decoding and the tools to analyze their behavior. We complete the chapter by summarizing the different techniques used for multiuser communications, since we consider networks with multiple sources. Furthermore, we give a brief overview of network coding which has recently been considered for wireless networks with relays and jointly combined with channel coding in order to achieve better performance and higher throughput. Chapter 3 introduces cooperative communications and the different aspects of cooperation. In this chapter we give an overview of several communication strategies for wireless relaying. We start by considering the relay channel which is the simplest form of cooperation and we summarize the existing distributed coding schemes for this model. We then consider a more general case, the MARC, and give an overview of a joint network and channel coding recently proposed in the literature for this channel. In this chapter, we restrict ourselves to the two-user MARC. We further consider a twouser cooperative scenario where the two users communicate with each other and each user acts as a relay for its partner. Beside giving an overview of the state-of-art, some contributions on the analysis of some existing schemes are provided in this chapter. In Chapter 4, we propose a distributed turbo-like coding scheme for a multi-source relay scenario where multiple sources communicate with a destination with the help of a common relay. The relay uses the decode-and-forward strategy and operates in half-duplex mode. In this chapter, we consider orthogonal scenarios. Orthogonality is

35 4 CHAPTER 1. INTRODUCTION obtained by means of time-division multiple-access (TDMA). The proposed distributed code can be viewed as a serially concatenated code (SCC). Thus, at the destination decoding is performed in an iterative fashion which resembles the decoding of a classic SCC. The proposed scheme achieves very low error rates and offers significant performance gains with respect to non-cooperation, even for a very large number of sources. Furthermore, it provides a high flexibility in terms of code rate, number of sources, overall system rate and error protection. Chapter 5 is devoted to the discussion of non-orthogonal scenarios where several nodes in a network are allocated the same bandwidth during the time. In this chapter, the distributed turbo-like coding scheme of Chapter 4 is combined with multiuser detection for the non-orthogonal MARC. The main results are summarized and conclusions are drawn in Chapter 6. Parts of this thesis have been published in [YG10], [YG11] and filed in a patent [GY09].

36 CHAPTER 2 Background and Basic Principles This chapter gives an overview of the basic concepts at the basis of the work of this thesis. The chapter is organized as follows. We shall start by introducing some required preliminaries for point-to-point communications. In Section 2.1 and Section 2.2, we present the wireless channel model that will be used in this thesis and we give information theoretic limits for channel coding. In Section 2.3, we describe the channel codes used in the sequel of the thesis: convolutional codes, parallel concatenated codes and serially concatenated codes. We further summarize the iterative decoding in Section 2.4 and Section 2.5 briefly describes the extrinsic information transfer (EXIT) charts used to analyze the performance of iterative decoding. In this chapter, we also address multiuser communications. Section 2.6 is devoted to briefly present the different approaches used in multiuser communications and to describe the technique adopted in our work for non-orthogonal scenarios. By nonorthogonal scenarios, we refer to networks where different nodes are allocated the same transmission time, therefore the destination receives a superposition of the transmitted signals. Finally, Section 2.7 gives a brief overview of network coding, a new concept recently introduced in network communication. 2.1 Channel Model for Wireless Communications In this section, we present the channel model considered in this thesis. Figure 2.1 illustrates a simplified functional diagram of a digital communications system, where 5

37 6 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Source Channel Encoder Modulator Channel Sink Channel Decoder Demodulator Figure 2.1 Block diagram of a digital communication system. the source encoder and the source decoder are included in the source and the sink, respectively. The data source generates messages which are transmitted to the receiver over a physical medium, or channel. The source transmits a packet u of length k, u = (u 1,u 2,...,u k ). The data u is encoded by a channel encoder which outputs a codeword c of length n, c = (c 1,c 2,...,c n ). The channel encoder adds redundancy to the data to make it more robust against errors and channel impairments. The channel code rate is defined as R c = k/n. In this thesis the elements of u and c are chosen from the binary Galois field GF(2), i.e., u i, c i {0,1}. The binary sequence c at the output of the channel encoder is passed to the modulator which maps the binary information sequence into signal waveforms that match the characteristics of the channel. It essentially prepares the encoded signals to be transmitted through the physical medium. In this thesis, we consider binary phase shift keying (BPSK) modulation. The modulated codeword, x, is sent over the channel. The destination receives the corrupted version y of codeword x. y = (y 1,y 2,...,y n ). The demodulator and the decoder try to recover the information packet u from y and generate an estimate û of the original packet u. In this thesis, we assume a wireless channel model with noise, which exhibits propagation path-loss and fading. In the following we briefly describe the channel impairments(noise, path-loss propagation and fading) before modeling the channel considered in this thesis Noise The additive noise channel is the simplest model for a communication channel. In this model, the transmitted signal is corrupted by an additive random noise. This noise may

38 2.1. CHANNEL MODEL FOR WIRELESS COMMUNICATIONS 7 be thermal and comes from electronic components and amplifiers at the receiver or it may arise from interference encountered during the transmission. The thermal noise is mathematically represented as a Gaussian noise process. We make the common assumption that this noise has power spectral density equal to N 0 /2. According to this model, the noise is called additive white Gaussian noise (AWGN) and the channel model is called the AWGN channel Path-Loss Propagation In wireless communications, signals traveling through space are susceptible to path-loss which translates into a reduction in power. In our work, we will consider networks with relays in which the position of the relay with respect to the source nodes and to the destination is given for a certain topology. Therefore, we are interested in calculating the ratio of the received power at distance d to the received power at a reference distance d ref. The Friis transmission equation [Rap99, Yac93] gives the ratio of the power received at the sink P r to the power at the transmitter P t, when the receiver and the transmitter are separated by a distance d, P r (d) P t = G r G t ( λ 4πd ) α (2.1) where α denotes the path-loss exponent and it is often assumed to be 2 α 6. For propagation in free space, the path-loss exponent α is assumed to be 2. For lossy environments, α can be in the range of 4. G r and G t denote the gains of transmit and receive antenna, respectively, and λ the wavelength of the signal. From (2.1), we can obtain the ratio of the received power at distance d to the received power at a reference distance d ref. This ratio is given by P r (d ref ) P r (d) = ( dref d ) α (2.2) IndB,thisratioisgivenby10αlog 10 (d ref /d).from(2.2),itfollowsthatthemeanpower of the signal decreases with distance d as d α. In our work, we will consider wireless relay networks. For instance, we consider a relay channel where the relay is at half distance from the source and the destination (d ref /d = 0.5). The source transmits to both the relay and the destination. If we assume a path-loss exponent α = 3.52 which is the value assumed for UMTS [HT01], the SNR advantage of the relay-to-destination channel with respect to the source-to-destination is equal to 10.6 db Fading In wireless communications, fading is due to multipath propagation through reflections or to shadowing by obstacles (hills, buildings, etc..). When signals arrive at the receiving antenna having traversed different paths, they may combine destructively.

39 8 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES This multipath phenomenon can induce signal fading. Fading is modeled differently according to the received signals at the sink. If the sink receives only the reflected signals i.e., only diffused components are present, fading is modeled with a Rayleigh distribution. The signal amplitude is therefore Rayleigh distributed. Fading can also be modeled as Ricean fading when besides the diffused components there is a specular direct component due to the line-of-sight connection between source and sink. In this thesis, we will consider fading which follows a Rayleigh distribution. The magnitude and the phase of the fading can change at different rates. Therefore, the fading can be fast or slow depending on the coherence time of the channel Channel Model We consider an AWGN channel with path-loss propagation and fading. The sink is at distance d of the source. The source transmits with power P. After modulation, the samples of the received signals at the sink are given by y = Hx+z (2.3) where x is the modulated sequence of the binary sequence c of length n. In the course of this thesis, we consider BPSK modulation, i.e., x i { 1,+1}. z is an AWGN noise vector of length n with zero-mean and variance σ, H is a [n n] diagonal matrix with Rayleigh fading channel coefficients h in the main diagonal and zeros everywhere else. For an AWGN channel, H is the identity matrix. The channel can be described by the transition distribution p(y x), where p() denotes the probability mass function (pmf) if y is discrete or the probability density function (pdf) if y is continuous with a slight abuse of notation. The instantaneous signal-to-noise ratio is defined as the ratio of the received power and the noise power. We denote by γ the energy per symbol to noise spectral efficiency, commonly known as E s /N 0, and by γ b the energy per bit to noise spectral efficiency, known as E b /N 0. γ is given by γ = h 2 P N 0 W (2.4) where W denotes the channel bandwidth. For binary coding and modulated system, γ and γ b are related by γ = γ b MR c (2.5) where R c is the code rate and M is the number of bits per modulation symbol. 2.2 Information Theoretic Limits Entropy and Mutual Information In this section, we introduce two relevant concepts in information theory, entropy and mutual information.

40 2.2. INFORMATION THEORETIC LIMITS 9 The entropy is a measure of the uncertainty of a random variable. Let X be a discrete random variable that takes values in an alphabet X and has probability mass function p(x) = Pr{X = x}, x X. The entropy H(X) of a discrete random variable X is defined by H(X) = x X p(x)log 2 p(x). (2.6) The joint entropy H(X,Y) of a pair of discrete random variables (X,Y) with joint distribution p(x, y) is defined as H(X,Y) = x X p(x,y), (2.7) and the conditional entropy of Y given the knowledge of X is given by y Y H(Y X) = p(x)h(y X = x) x X = p(x,y)log 2 p(x y). x X y Y (2.8) In the continuous domain, the entropy of a random variable becomes the differential entropy. The differential entropy h(x) of a continuous random variable X with density p(x) is defined as h(x) = p(x)log 2 p(x)dx, (2.9) S where S is the support set of the random variable. The mutual information is a measure of the amount of information that one random variable contains about another random variable. It represents the reduction in the uncertainty of one random variable due to the knowledge of the other. For a pair of discrete random variables (X, Y) with a joint distribution p(x, y) and marginal probability mass functions p(x) and p(y), the mutual information is given by I(X;Y) = x X y Y p(x,y)log 2 p(x,y) p(x)p(y). (2.10) It follows from the definitions of entropy and mutual information that I(X;Y) = H(X) H(X Y). (2.11) For continuous random variables, the mutual information is given by I(X;Y) = p(x,y) p(x,y)log 2 dxdy. (2.12) p(x)p(y)

41 10 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Channel Capacity In this section, we introduce the limits for channel coding. In his pioneering work, Shannon established the basic limits of information communication [Sha48]. The channel capacity is defined as the maximum rate of information that can be transmitted reliably through the channel. For a communication channel with input X and output Y, the capacity C is defined as C = maxi(x;y). (2.13) p(x) The channel capacity of an AWGN channel with signal-to-noise ratio γ is given by C(γ) = log 2 (1+γ) bits per channel use (2.14) under the assumption that the input variables are Gaussian distributed. For constrained input variables, i.e., the channel input variables do not follow a Gaussian distribution, the input variables will be drawn from a discrete alphabet X. The capacity under these constraints can be numerically computed using the following formula C(γ) = max p(x) x X + p(y x i ) p(y x i )p(x i )log 2 dy. (2.15) p(y) Figure 2.2 depicts the capacity C(γ) with Gaussian distributed inputs and BPSK modulation of an AWGN channel. The spectral efficiency η of a modulation set is the number of bits per second per Hertz that the set can support. Let R = R c M be the total rate, where R c and M are defined in Section For Gaussian inputs, we have Substituting γ by γ b R, we have R C = log 2 (1+γ). (2.16) R log 2 (1+γ b R). (2.17) The spectral efficiency η is the unique solution of the equation η log 2 (1+γ b η). (2.18) The values of η which satisfy (2.18) with equality are given by the curve labeled Gaussian inputs (dashed line) in Figure 2.3 as a function of γ b. The other curve (solid line) in Figure 2.3 corresponds to the spectral efficiency with BPSK modulation Outage Probability In wireless communications, channels can exhibit different kinds of fading. When the fading is slow, we speak about block fading channels. By slow fading, we mean that the

42 2.2. INFORMATION THEORETIC LIMITS 11 4 Gaussian inputs BPSK 3 bits/use γ [db] Figure 2.2 Channel capacities in bits per second for Gaussian input variables and BPSK modulation over AWGN channel. 4 Gaussian inputs BPSK 3 bits/use/hz γ b [db] Figure 2.3 Spectral efficiencies in bits per second per Hertz for Gaussian input variables and BPSK modulation over AWGN channel. fading coefficient is constant over one frame duration. For block fading channels, the

43 12 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES 10 0 Gaussian inputs BPSK Outage Probability γ [db] Figure 2.4 Outage probability for Gaussian distributed input variables and BPSK modulation for a rate R = 1/2 over Rayleigh block fading channel. capacity is a random variable. Therefore it is more meaningful to consider the outage probability rather than the capacity. For a data rate R, whenever the channel capacity C is greater than R, it is possible to find a code which achieves an arbitrarily low error probability. When C is lower than R, then we say that the channel is in outage. We define the outage probability as follows P out = Pr(C < R). (2.19) Notice that the above equation does not mean that in average we achieve a spectral efficiency equal to R, but it means that the frame error rate (FER) is greater than or equal to P out if the frame has a spectral efficiency equal to R. Indeed, the outage probability represents a lower bound on the FER. Figure 2.4 shows the outage probability for a rate R = 1/2 with Gaussian input variables and with BPSK modulation. 2.3 Channel Coding Channel coding is used in digital communication systems in order to achieve reliable communication. The basic principle is to introduce some redundancy bits to the information data to be transmitted. These additional bits may allow detection and correction of bit errors in the received data, providing therefore more reliable information transmission. On the other hand, the use of channel coding implies a reduction in data rate or an expansion in bandwidth.

44 2.3. CHANNEL CODING 13 D D D Figure 2.5 Rate 1/2 recursive systematic convolutional code with memory ν = 3 In this section, we describe some channel codes considered throughout the thesis. We start by briefly describing convolutional codes, and then we introduce two basic structures of concatenated codes: parallel concatenated codes and serially concatenated codes Convolutional Codes Convolutional codes were first introduced by Elias in [Eli55] as a family of codes simple to implement and achieving good performance. Let us consider a convolutional encoder with p input bits and q output bits. Each block of q bits depends linearly not only on the p bits at the input but also on the ν previous blocks. Hence, this convolutional encoder introduces a memory effect of order ν. Different representations are used to illustrate this memory effect, like trellises and state diagrams. These representations are adapted to the decoding algorithms. The trellis representation is the most commonly used. Figure2.5 depictstheblockdiagram ofaconvolutional encoderwith memory ν = 3. D represents the memory element; it forwards the bits with a delay of one time unit. One can see that the input being encoded is included in the output sequence. Such a code is referred to as systematic, otherwise the code is called non-systematic. The code is recursive because the current memory bits are fed back to compute the new memory bits. This code has a rate R = 1/2 which corresponds to one redundancy bit for each information bit. The generator polynomials in octal form of the recursive convolutional code of Figure 2.5 are (13,15) 8. For more general description of convolutional codes, we refer to [LC04]. There are many algorithms to decode a convolutional code. We will focus on softinput soft-output (SISO) decoders. The most common algorithms are the soft-output Viterbi algorithm (SOVA) [HH89], the BCJR algorithm [BCJR74], also known as the MAP algorithm, which maximizes the a posteriori probability and the log-map algorithm [RVH95] which is a version of the MAP algorithm in the logarithmic domain. Since the log-map algorithm has high complexity, a suboptimal variant of this algorithm, the Max-log-MAP algorithm [RVH95] is used. The Max-log-MAP algorithm is a simplification of the log-map algorithm where the logarithmic operation is replaced by a maximization function (log(exp(a)+exp(b)) max(a,b)). In this thesis, we use

45 14 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Encoder Encoder Figure 2.6 Block diagram of a PCC. Outer Code Inner Code Figure 2.7 General block diagram of an SCC. the MAP decoder for simulation results Parallel Concatenated Codes Powerful codes may be constructed by code concatenation. The concept of concatenated codes was first introduced by Forney [For66]. Examples of such codes are the parallel concatenated codes(pccs)[bgt93, BG96] and the serially concatenated codes(sccs) [For66, BM96]. PCCs were introduced by Berrou [BGT93] in The original PCC, as introduced in [BGT93], consists of the concatenation of two convolutional codes and was called turbo code due to the iterative decoder structure. The turbo codes were the first practical codes approaching the channel capacity given by Shannon [Sha48]. Since their invention, turbo codes have raised a great interest in the coding community and have been adopted in several communication systems like UMTS, WiMAX, CDMA 2000 and Digital Video Broadcasting (DVB). Figure 2.6 shows the block diagram of a PCC. A PCC consists of two constituent encoders C 1 and C 2 linked by an interleaver Π. The information bits at the input of the first encoder C 1 are scrambled by the interleaver before entering the second encoder C 2. In the course of this thesis, we will consider concatenation of convolutional codes. PCCs present very good performance at low and medium SNRs. For instance, for rate R = 1/2, PCC can achieve a frame error rate (FER) less than 10 5 and perform within 0.35 db from capacity. However, it is well known that the performance of PCCs may not be so good at very high SNRs Serially Concatenated Codes The structure of an SCC is depicted in Figure 2.7. An SCC consists of the cascade of an outer encoder C O, an interleaver Π which permutes the bits of the outer codewords and

46 2.3. CHANNEL CODING 15 M U X Figure 2.8 Block diagram of the SCC introduced in [GMV05, GMV09]. S P C rate-1/2 rate-1 Figure 2.9 Flexicode encoder block diagram. an inner encoder C I whose input information is the permuted outer codeword [BM96]. SCCs may outperform PCCs especially at very low error rates. We will restrict our interest to a novel class of serially concatenated convolutional codes (SCCCs) introduced in [GMV05, GMV09]. The structure of this novel class is depicted in Figure 2.8. The information sequence u is first encoded by an encoder C a followed by a puncturer P a. The resulting codeword is interleaved by interleaver Π and passed to encoder C b. In [GMV05, GMV09], while no assumption is made for C a, C b is required to be systematic and recursive. The sequence at the output of C b is punctured by puncturers Pb s and Pp b for systematic and parity bits, respectively. In standard SCCCs, high rates are obtained by heavy puncturing of the outer code. In this novel class of SCCCs, the heavy puncturing is moved to the inner code, which can be punctured beyond the unitary rate. This coding scheme allows keeping a very low error floor for a wide range of code rates since the interleaver gain is preserved, and achieves much better performance than standard SCCs, especially for high rates. In Chapter 4, a distributed coding strategy inspired by this coding scheme is proposed for wireless networks with relays FlexiCode A new turbo-like code called FlexiCode was introduced in [CTD + 05]. The functional block diagram of the Flexicode encoder is depicted in Figure 2.9. The Flexicode as presented in [CTD + 05] considers the concatenation of convolutional codes. The user data is first encoded by encoder C O. The rate of C O is fixed at 1/2. The bits at the

47 16 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES output of encoder C O are then interleaved, grouped into groups of J bits and passed to a single parity check (SPC) circuit. This simply forms the sum modulo-2 of the J bits. The bits at the output of the SPC circuit are then encoded by a convolutional encoder C I of rate-1. The FlexiCode is a systematic code, therefore the information bits are also transmitted directly over the channel. Thus, the overall rate of the FlexiCode is J/(J +1). Varying parameter J allows to change the code rate and the performance of the FlexiCode. The FlexiCode presents good error floor performance. It can achieve a bit error rate (BER) below for a broad range of code rates (even for rates as high as 0.95) and block sizes. Some FER curves are presented in Section A distributed coding strategy for multiuser cooperative relay networks inspired by this coding structure is proposed in Chapter Iterative Decoding of Concatenated Codes With the successful proposal of turbo codes, a decoding scheme based on iterative decoding was introduced in [BGT93]. Another approach of iterative decoding was also introduced in [LYHH93] in the context of the concatenation of convolutional codes and simple block codes. Iterative decoding as described in [BGT93] is performed between the component decoders which exchange information during iterations. In the iterative decoding procedure, each component decoder generates a reliability value for each information and/or code symbol. This reliability represents the extrinsic information of the component decoder and is then passed to the other decoder. By extrinsic information we mean that each decoder has to be fed with information which does not originate from itself. This information indicates the amount of new information obtained through the code structure and is regarded as a priori information to the other decoder in the next iteration. The error probability performance of turbo-like codes behaves in a similar manner to the curve shown in Figure The region called the waterfall region corresponds to theregionwhereaveryrapidreductionoftheerrorprobabilitywithγ b isobserved.this region is followed by the error floor region where shallower reduction in error probability is observed. In this region, the performance of the turbo-like code is dominated by its minimum Hamming distance d min (the minimum Hamming distance between any two codewords) and its multiplicities. The error floor can be analytically estimated if d min is known [GPB01]. A natural reliability value for the exchange of soft information is in the form of logarithm likelihood ratio (LLR). Before detailing the iterative decoding process, we will briefly describe the LLR.

48 2.4. ITERATIVE DECODING OF CONCATENATED CODES 17 Figure 2.10 Typical behavior of turbo-like codes The Logarithm Likelihood Ratio Consider the variable x { 1;+1}. The a priori LLR value of x is defined as L a (x) = log p(x = +1) p(x = 1). (2.20) L a (x) represents the a priori knowledge about the random variable x. Consider a transmission channel with transition probability p(y x). The a posteriori LLR value of x, conditioned on received data y, is L(x y) = log p(x = +1 y) p(x = 1 y). (2.21) The sign of L(x y) provides the hard decision on x and the value L(x y) measures the reliability of the decision. Applying Bayes rule yields, p(x = +1 y) = p(y x = +1) p(x = +1), (2.22) p(y) where p(x = +1) is the a priori probability that x = +1 was transmitted. From (2.21) and (2.22), we have L(x y) = log L ch (y x) = log p(x = +1) p(y x = +1) +log p(x = 1) p(y x = 1) = L a(x)+l ch (y x). (2.23) For an AWGN channel, the channel LLR L ch (y x) is given by ( ) 1 exp 2πσ (y 1)2 2 2σ 2 p(y x = +1) p(y x = 1) = log ( ) = 1 exp 2πσ (y+1)2 2 2σ 2 2y σ 2 (2.24)

49 18 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Decoder -1 Decoder Figure 2.11 Iterative decoding of a PCC. For a channel with Rayleigh fading the LLR L ch (y x,h) is given by where h denotes the Rayleigh coefficient. L ch (y x,h) = 2yh σ 2 (2.25) Iterative Decoding of a PCC The iterative decoding principle of a PCC is shown in Figure Decoder C1 1 is the SISO decoder corresponding to encoder C 1 and decoder C2 1 corresponds to encoder C 2. In the sequel, we consider the concatenation of two convolutional codes. The corresponding decoders use the BCJR algorithm. We denote by L e1 (u) and L e2 (u) the extrinsic information passed by C1 1 and C2 1, respectively, and by L a1 (u) and L a2 (ũ) the a priori information at the input of C1 1 and C2 1, respectively. Turbo decoding starts by processing the first SISO decoder C1 1. C1 1 computes the a posteriori LLRs L(u). At the first iteration, no a priori information L a1 (u) is available. Next, C2 1 is processed. C2 1 is fed by the channel observation from the demodulator and the a priori information L a2 (ũ) from C1 1. L a2 (ũ) is the interleaved version of L e1 (u) and L e1 (u) = L(u) L a1 (u). In its turn, C2 1 computes the a posteriori probability L(ũ) and forwards extrinsic information L e2 (ũ) = L(ũ) L a2 (ũ) to C1 1. C1 1 is processed again in the next iteration round taking into account the a priori information provided by the second decoder. This process is repeated until a fixed maximum number of iterations is reached or an early stopping criterion is fulfilled. In Figure 2.12, we show the BER curve results for a PCC. We consider the concatenation of two convolutional codes. The 4-state, rate-1/2, recursive convolutional code with generator polynomials (5,7) 8 is used for encoders C 1 and C 2. A maximum of 10 iterations is performed and a frame of length k = 1504 bits is considered. The waterfall

50 2.4. ITERATIVE DECODING OF CONCATENATED CODES uncoded PCC R=1/ BER 10-4 Waterfall region Error floor region γ b [db] Figure 2.12 BER curve of A PCC over an AWGN channel, R = 1/2, k = 1504 bits, 10 iterations. -1 Decoder Decoder - - Figure 2.13 Iterative decoding of an SCC. region of the turbo code corresponds approximately to the SNR region db. In Figure 2.12, the slope change (error floor) is observed between 10 5 and 10 6 of BER Iterative Decoding of an SCC The iterative decoder of an SCC is depicted in Figure We denote by L eo (c) and L ei (c) the extrinsic information passed by C 1 O and C 1 I, respectively, and by L ao (c) and L ai (c) the a priori information at the input of C 1 O and C 1 I, respectively. The inner decoder C 1 I uses the channel observation and the a priori information L ai (c) (which is zero in the first iteration) to compute the a posteriori LLRs L( c), the interleaved version of L(c). It then forwards the extrinsic information L ei ( c) = L( c) L ai ( c) to the outer decoder C 1 O. C 1 O uses only L a O (c) = Π 1 (L ei ( c)) since no channel observation is available for the outer decoder. It then computes the a posteriori LLRs L(c) and feeds back to the inner decoder C 1 I the extrinsic information L eo (c) = L(c) L ao (c).

51 20 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES uncoded SCC R=1/2 PCC R=1/ BER γ b [db] Figure 2.14 BER curves comparison between an SCC and a PCC over AWGN channel, R = 1/2, k = 1504 bits, 10 iterations. The PCC suffers from an error floor between BER 10 6 and Decoder Decoder Decoder SPC -1 Figure 2.15 Iterative decoding of a FlexiCode This process is repeated iteratively until a stopping criterion is satisfied or until a fixed number of iterations is reached. In Figure 2.14, we compare the performance of an SCC and a PCC with the same rate (R = 1/2) and complexity (10 iterations). Here, we consider the concatenation of two convolutional codes. As the curves show, the performance of the PCC is better than that of the SCC for high values of the bit error probabilities (waterfall region) while the PCC suffers from an error floor between BER 10 6 and Below BER 10 6, the SCC behaves significantly better than the PCC. For the SCC, at BER=10 6 the floor is not yet observed Iterative Decoding of a FlexiCode The block diagram of the FlexiCode decoder is shown in Figure Since the FlexiCode considers the concatenation of convolutional codes, the outer decoder C 1 O and the inner decoder C 1 I use a SISO BCJR decoding algorithm. The channel metrics

52 2.4. ITERATIVE DECODING OF CONCATENATED CODES Flexicode R=1/2 Flexicode R=2/3 Flexicode R=5/ FER γ b [db] Figure 2.16 FER performance after 10 iterations for R = 1/2,2/3 and 5/6 with k = 1504 bits. An AWGN channel is assumed with BPSK modulation. for the systematic bits are passed to decoder C 1 O, and the channel metrics for the parity bits are passed to decoder C 1 I. The outer code C O is first decoded by decoder which generates extrinsic information used at the input of the SPC decoder after proper interleaving. The SPC decoder is decoded in the outer-inner direction. It uses the well-known message-passing algorithm[gal62] and generates soft outputs which are then passed to the inner SISO decoder C 1 I. The inner decoder C 1 I decodes the inner code C I using the extrinsic information provided by the SPC. C 1 I generates extrinsic information which is passed to the SPC decoder. Next the SPC code is decoded in the inner-outer direction, using the soft outputs of C 1 I. These SPC soft outputs are then deinterleaved and input to decoder C 1 O. The process repeats until a fixed number of iterations is reached or a certain stopping criterion is fulfilled. C 1 O Figure 2.16 shows the FER performance of the FlexiCode [CTD + 05] for different code rates (R = 1/2,2/3 and 5/6). Ten iterations are simulated and a frame length k = 1504 bits is considered. As shown in Figure 2.16, the FlexiCode has not still reached the floor at FER The SCC proposed in [GMV05, GMV09] presents some similarities with the FlexiCode in the sense that a serial concatenation of an outer and an inner convolutional code, concatenated through an interleaver, is considered but in place of using a SPC code to obtain rate variability, the use of a puncturing device is proposed.

53 22 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES 2.5 Extrinsic Information Transfer Charts Generally the turbo decoding algorithm does not converge to a maximum likelihood solution, although in practice it gives good error correction performance. One way to study the convergence behavior is to use EXIT charts, introduced by ten Brink in [tb01b]. In this thesis, we use EXIT charts to analyze the performance of iterative decoding from the convergence behavior point of view. In the following, we briefly describe the concept of EXIT charts and explain their construction methodology. EXIT charts are an analytical technique to describe the flow of extrinsic information between two (or more) constituent decoders. In an EXIT chart, the mutual information transfer characteristics of the component decoders are plotted to describe the turbo decoding graphically and to predict the SNR values corresponding to the start of the turbo waterfall region. To explain the construction methodology, we will consider, as an example, the decoder of the SCC in Figure As explained in Section 2.1.4, the received signal at the decoder input for an AWGN channel is The conditional probability density function of y given x is ( ) 1 p(y x) = exp (y x)2 2πσ 2 2σ 2 The channel LLR value is denoted by L ch and is given by L ch = log After simplification of (2.28), we have y = x+z (2.26) (2.27) p(y x = +1) p(y x = 1). (2.28) L ch = µ L x+z L (2.29) where µ L = 2/σ 2 and z L is Gaussian distributed with zero mean and variance σl 2 = 4/σ 2. We denote by I(L ch,x) the mutual information between the transmitted symbol x and the LLR L ch. I(L ch,x) is given by I(L ch,x) = 1 2 x=+1;x= 1 + It can be shown that [Hag04] 2p L (l X = x) p L (l X = x)log 2 dl. (2.30) p L (l X = 1)+p L (l X = 1) I(L ch,x) = 1 E [ log 2 (1+exp L ch ) ] (2.31) where E denotes the expectation. By invoking the ergodicity theorem, i.e., the expectation can be replaced by the time average, the mutual information can be measured by taking a large number N of samples. Therefore, I(L ch,x) can be computed by I(L ch,x) = 1 1 N N log 2 (1+exp xnln ). (2.32) n=1

54 2.5. EXTRINSIC INFORMATION TRANSFER CHARTS ,9 Outer Code, Rate=1/2, (07,05) Inner Code, Rate=1, (03,02) 0,8 0,7 IO(A,X), II(E,X) 0,6 0,5 0,4 γ b =1.1 db 0,3 0,2 0, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 I O(E,X), I I(A,X) Figure 2.17 EXIT Chart of the SCC: rate-1/2 outer convolutional code of generator polynomials (07,05) and rate-1 inner convolutional code of generator polynomials (03,02) We denote by I(L a,x) the mutual information between the transmitted symbol x and the a priori LLR L a and by I(L e,x) the mutual information between the transmitted symbol x and the extrinsic information L e. The information transfer function T is measured as I(L e,x) = T(I(L a,x)) (2.33) According to (2.32), I(L e,x) and I(L a,x) can be computed assuming that the a priori LLRs L a are modeled as independent Gaussian random variables [tb01b]. For each component decoder C 1 O and C 1 I, we can compute its transfer function and then plot both functions in a two-dimensional chart. The a priori information I I (A,X) of the first decoder is plotted on the horizontal axis and its corresponding output extrinsic informationi I (E,X)isplottedontheverticalaxis.Fortheseconddecoder,thea priori information I O (A,X), which is equal to I I (E,X), is plotted on the vertical axis and its output extrinsic information I O (E,X), which will be the a priori information I I (A,X) in the next iteration, is plotted on the horizontal axis. By stepping between the two curves, we can illustrate the iterative exchange of extrinsic information between the outer and the inner decoder. For a successful decoding, there must be an open tunnel betweenthecurves.theminimumvalueofγ b forwhichweobserveaclearpathbetween the curves corresponds the convergence threshold. Figure 2.17 shows the trajectory of the iterative decoding at γ b = 1.1 db for an SCCC with the 4-state, rate-1/2, recursive convolutional code with generator polyno-

55 24 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES mials (1,5/7) 8 used as outer code C O, and the 2-state, rate-1, recursive convolutional component code with generator polynomial (1,3/2) 8 used as inner code C I. At γ b = 1.1 db, an open tunnel is observed between the curves. This value of γ b corresponds to the convergence threshold. 2.6 Multiuser Transmission In mobile radio communications, the objective is to allow multiple users to access the services provided by an operator. In multiuser communications, different techniques have been proposed to efficiently use the available resources. These techniques can be classified into orthogonal and non-orthogonal approaches. For radio systems there are two main resources available, frequency and time. Division by frequency, so that each user is allocated part of the spectrum for all the time, results in frequency division multiple access (FDMA). Division by time, so that each user is allocated all of the spectrum for part of the time results in time division multiple access (TDMA). TDMA and FDMA are orthogonal techniques where signals from different users are orthogonal to each other, i.e., their cross correlation is zero. Non orthogonal approaches allow nonzero correlation among signals from different users such as in coded division multiple access (CDMA) [GJP + 91]. In CDMA, each user is allocated the entire spectrum all of the time. CDMA uses codes to identify the different users. Another technique of multiple access, called interleaved division multiple access (IDMA) was proposed in [PLWL03a] and can be considered as a special case of the CDMA technique. In IDMA, the different sources are distinguished by means of interleavers Frequency Division Multiple Access In FDMA, each source is allocated a different frequency bandwidth in order to allow simultaneous transmissions. As shown in Figure 2.18, the channel bandwidth is divided into q = 3 sub-bandwidths, where q denotes the number of sources Time Division Multiple Access In TDMA, each source is allocated a specific time slot as shown in Figure At the receiver, the signal of each source is detected during its corresponding time slot, therefore the TDMA technique requires perfect synchronization between the sources. TDMA is used in the digital 2G cellular systems such as the Global System for Mobile Communications (GSM). In this thesis, we will consider TDMA for orthogonal scenarios.

56 2.6. MULTIUSER TRANSMISSION 25 Spectral Density time User1 User2 User3 frequency Figure 2.18 Multiplexing principle of FDMA Spectral Density time User3 User2 User1 frequency Figure 2.19 Multiplexing principle of TDMA Coded Division Multiple Access CDMA employs spread-spectrum technology and a special coding scheme where each transmitter is assigned a spreading code to allow multiple users to be multiplexed over the same physical channel. All users are allowed to transmit simultaneously in the same frequency bandwidth. The modulated coded signal has a much higher data bandwidth than the original data. Although the available resources are exploited optimally, the difficulty is in the separation of the signals of each user at the receiver. For multiuser detection, a specific spreading code is allocated to each user allowing therefore the separation of the signals at the receiver. Figure 2.20 depicts the CDMA principle of multiplexing. This technique of multiple access has been adopted in 3G mobile technology standards as CDMA2000 [CDM].

57 26 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Spectral Density time User3 User2 User1 frequency Figure 2.20 Multiplexing principle of CDMA AWGN Spreading Code Figure 2.21 Block diagram of an IDMA transmitter Interleaved Division Multiple Access IDMA was proposed by Li Ping et. al. in [PLWL03a]. Like CDMA, the IDMA technique allows the same bandwidth of frequencies to be allocated for multiple users that transmit simultaneously. However, unlike CDMA, all users in IDMA systems use the same spreading code. The separation between users is obtained by using a different interleaver for each user. In this thesis, we consider networks with multiple sources. For the scenarios where all sources transmit simultaneously, we adopt the IDMA technique for multiuser separation. With respect to CDMA, IDMA presents a low cost receiver which will be described in detail in Section IDMA transmitter We consider an IDMA system where q sources transmit simultaneously to a single destination. The structure of an IDMA transmitter at each source s i is depicted in Figure Each source s i encodes its information sequence u si of length k i by encoder C i of rate R i into codeword c si of length n i = k i /R i. The sequences c si are then spread by using a repetition code into sequences c s i of length n sp i = mn i, where m is the spreading factor. The code rate after spreading is denoted by R sp i = R i /m. Finally, each sequence c s i is scrambled by interleaver π i into the so-called chip sequence c s i. The key principle of IDMA is that the interleavers are different for different users. The received signal y at the destination is the superposition of the chip sequences

58 2.6. MULTIUSER TRANSMISSION 27 Figure 2.22 Block diagram of an IDMA receiver. x si weighted by the channel coefficients from the different sources, where x si denotes the BPSK modulated sequence of the binary sequence c s i. The received signal is given by q y = H i x si +z, (2.34) i=1 where H i is matrix of channel coefficient for source s i, and z is a vector of AWGN with variance σ IDMA receiver The destination receives a superposition of the signals transmitted by all users. At the receiver, an iterative decoding algorithm is performed using the chip-by-chip detection strategy [PLWL06] to recover the information of all users. In IDMA, the interleavers disperse the coded sequences and facilitate therefore the simple chip-by-chip detection scheme described in [PLWL06]. For a certain user, this detection algorithm consists of computing an estimate of the interference generated by the other users, and subtracting it from the received signal. Figure 2.22 illustrates the receiver in an IDMA system of q sources. The IDMA receiver consists of an elementary signal estimator (ESE) that exchanges extrinsic information with q a posteriori probability (APP) decoders, C 1 i, i = 1,...,q. Let L e,c 1(x si (t)) = log i ( ) Pr(xsi (t) = +1) Pr(x si (t) = 1) be the extrinsic a posteriori LLR generated by decoders C 1 i (2.35) for user s i, and

59 28 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES L e,ese (x si (t)) the extrinsic information generated by the ESE. The ESE computes the extrinsic information L e,ese (x si (t)) using the chip-by-chip detection algorithm [PLWL06]. During the iterative decoding process, this information is used after proper de-interleaving as the a priori information at the input of the decoders C 1 i. APP decoding is then performed by decoders C 1 i to generate the LLRs L e,c 1(x si (t)) which i will be used by the ESE after been properly interleaved in the next iteration. The process is iterated until the maximum number of iterations is reached or an early stopping criterion is fulfilled. The chip-by-chip detection algorithm is briefly described in the following. For each user s i, we can write the received signal y as where y(t) = h i x si (t)+ζ i (t) (2.36) ζ i (t) = i i h i x si (t)+z(t) (2.37) ζ i (t) represents the distortion (interference and noise) contained in y(t) with respect to user s i. Applying the central limit theorem, ζ i (t) can be approximated by a Gaussian variable with mean E(ζ i (t)) and variance Var(ζ i (t)). If mean E(ζ i (t)) and variance Var(ζ i (t)) are available, x si (t) can be estimated from (2.36). We list below the chipby-chip detection algorithm. Algorithm 1 Chip-by-Chip Algorithm: 1: Initialize L e,c 1(x si (t)) = 0 i,t i 2: E(x si (t)) = tanh(l e,c 1(x si (t))/2) i,t i 3: Var(x si (t)) = 1 (E(x si (t))) 2 i,t 4: E(ζ i (t)) = i i h i E(x s i (t)) t 5: Var(ζ i (t)) = i i h i 2 Var(x si (t))+σ 2 t 6: L e,ese (x si (t)) = 2h i (y(t) E(ζ Var(ζ i (t)) i(t))) i,t The IDMA technique presents a low-cost multiuser detection (MUD). Also, it presents several benefits in terms of robustness and diversity in multipath environments and very high spectral efficiency. With respect to TDMA, it is demonstrated that IDMA presents higher spectral and power efficiency in fading environments [WXP06]. In [WXP06], the authors provided a comparison between orthogonal (TDMA, FDMA) and non orthogonal approaches (CDMA, IDMA). For applications which are delay insensitive, e.g. , orthogonal schemes are advantageous while for delay sensitive services, e.g., speech and video, non orthogonal schemes are advantageous. In nonorthogonal schemes, a key advantage of IDMA over CDMA is that, in general, the complexity of a CDMA multiuser detector or soft interference cancellation detector is polynomial with the number of users [WP99]. In contrast, IDMA lends itself to a simple chip-by-chip detection algorithm whose complexity grows only linearly with the number of users [PLWL03b, PLWL03a].

60 2.7. NETWORK CODING 29 Figure 2.23 The butterfly network with routing: a multicast rate of 1.5 bits per unit time is achieved. 2.7 Network Coding In the traditional model of a network, the nodes operate as store-and-forward routers which transmit packets over point-to-point links. Another possibility is to combine, or encode, any of the received information and symbol streams. This is known as node coding. Network coding is a class of node coding where nodes receive and transmit linear combinations of packets in the form of strings of symbols. Network coding can be associated with cooperative communications as it employs intermediate nodes to combine packets, and some approaches have been established to introduce network coding strategies into relaying. An overview of these approaches will be presented in the next chapter. In this section, we summarize the basic idea of network coding based on the seminal work [ACLY00]. Network coding is a recent field in information theory where intermediate nodes are allowed to process incoming packets prior to forwarding, leading to improvements in throughput as compared to routing [ACLY00]. Figure 2.23 and Figure 2.24 depict the canonical butterfly network where source s multicasts its information to receivers y and z. Each link is assumed to have unit capacity. Figure 2.23 shows a way of multicasting 3 bits, b 1, b 2 and b 3, from node s to nodes y and z in 2 time units. It achieves a multicast rate of 1.5 bits per unit time, which is the maximum possible rate when the intermediate nodes perform just bit replication [Yeu02]. Figure 2.24 illustrates a different way to multicast two bits from the source node s to nodes y and z. Instead of simply replicating b 1 and b 2 in two different time slots, node w derives from the received bits b 1 and b 2 the exclusive-or bit b 1 b 2. w forwards b 1 b 2 to node x, which then broadcasts it to both y and z. At nodes y and z, bits b 2 and b 1 can be recovered, respectively, by a simple operation and a multicast rate of 2 bits

61 30 CHAPTER 2. BACKGROUND AND BASIC PRINCIPLES Figure 2.24 The butterfly network with network coding: a multicast rate of 2 bits per unit time is achieved. per unit time is achieved. As shown in this example, network coding allows to achieve higher throughput than routing. Moreover, all links are used once and a channel use is saved through network coding. Thus, network coding offers the potential advantage of minimizing both latency and energy consumption. In [LYC03], it was shown that linear network coding with finite alphabet size is sufficient to achieve the multicast capacity. Network coding was considered following two approaches: The deterministic network coding where knowledge about the complete network is assumed and each node is assigned a specific code operation [KM03]. The randomized network coding where the network changes permanently and each node performs random linear coding operations of the available blocks it receives from the other nodes [HKM + 03, HMK + 06]. In general, network coding assumes networks with error free channels. However, for practical implementation in real-world networks, network coding has to incorporate some error correcting capabilities to correct transmission errors. For instance, wireless links are subject to fading and interference. It is therefore a key issue to design error correcting codes for these networks in order to turn theoretical benefits into practice. Recently, the application of network coding to wireless networks has been considered as a way for providing users with cooperative diversity [XFKC07, HSOB05, YK07]. In [XFKC07], a network coding approach to cooperative diversity was proposed based on the algebraic superposition of channel codes over a finite field. Joint networkchannel coding/decoding schemes for the multiple-access relay channel were proposed in [HSOB05, YK07]. These coding schemes will be presented in detail in the next chapter.

62 2.8. CONCLUSIONS Conclusions In this chapter, we presented background knowledge about information theory, channel coding and decoding which is required for the next chapters. In this thesis, we will consider networks with multiple sources, therefore we also summarized the different techniques used for multiuser communications. Furthermore, we gave a quick overview of network coding which has recently been considered for wireless networks with relays and jointly combined with channel coding in order to achieve better performance and higher throughput.

63

64 CHAPTER 3 Cooperative Communications in Wireless Networks The essential goal of communication systems has always been to enable reliable communication with high data rates. In recent years, cooperative communications for wireless systems have attracted enormous attention. The basic idea of cooperative communications is that, exploiting the inherent broadcast nature of the wireless channel, all nodes in a wireless network can help each other to transmit information to the destination. Unlike conventional point-to-point communications, this new paradigm offers tremendous advantages such as higher throughput and significant reliability. In this chapter, we introduce the basic concepts of cooperative communications and the different aspects of cooperation. The aim of this chapter is to give an overview of several communication strategies for wireless relaying. We consider three different topologies of cooperative networks: the relay channel, the MARC, and the two-user cooperative topology. We start by considering the simplest form of cooperation which is the relay channel. We give an overview of some existing distributed coding schemes for the relay channel. We next consider a more general case, the MARC, and give an overview of joint network and channel coding schemes for this channel proposed in [HD06, YK07]. In this chapter, we restrict ourselves to the two-user MARC. We further consider a two-user cooperative scenario where the two users communicate with each other and each user acts as a relay for its partner. The remainder of this chapter is organized as follows. In Section 3.1, we describe the relay channel, its different cooperation strategies, the achievable rates by a particular encoding strategy and the outage probability over block fading channels. Besides the 33

65 34 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS Figure 3.1 The relay channel: a three terminal channel theoretical aspects, we also describe two distributed coding strategies recently proposed for the relay channel: the distributed parallel concatenated codes and the distributed serially concatenated codes. In Section 3.2, we present the two-user time division MARC and give information theoretic limits in terms of achievable rates and outage. We further summarize different encoding strategies which investigate network and channel coding. In Section 3.3, we describe the two-user cooperative scenario and we focus on a network coding approach recently proposed for this scenario. Beside describing the state-of-art, this chapter contains two contributions. These contributions are the analysis of some existing schemes rather than new proposals. For the two-user MARC, we consider the encoding scheme in [YK07] where soft information is processed at the relay and we establish a comparison between processing soft information and hard information at the relay depending on the channels conditions. For the two-user cooperative topology, we consider an non-orthogonal scenario where IDMA is used for multiuser detection. 3.1 The Relay Channel The discussion of cooperative communications can be traced back to the 70s when van der Meulen proposed the relay channel [vdm71]. The relay channel is a three terminal channel: it consists of a source node which communicates with a single destination aided by a relay node. Due to the broadcast nature of wireless channels, the signal sent by the source is overheard by the relay. Therefore, the relay may help in improving the communication between the source and the destination by sending additional information about the source signal. The relay channel was further investigated by Cover and El Gamal in [CG79], where upper and lower bounds to the capacity where derived, and two basic coding strategies were proposed: decode-and-forward and compress-andforward, where the relay decodes and compresses, respectively, the source information prior to forwarding. Figure 3.1 depicts the relay channel model. As illustrated in Figure 3.1, the source broadcasts its encoded information to the destination and the relay. The relay receives a noisy version of the source codewords. It then processes the received signal before

66 3.1. THE RELAY CHANNEL 35 transmitting a new version of the original message according to different strategies. The main three strategies are stated in the following: Amplify-and-forward (AF): In the amplify-and-forward scheme, the relay simply retransmits a scaled version of the signal it has received subject to the power constraint at the relay. The main drawback of this strategy is that amplifying the signal will also amplify the noise at the relay. Decode-and-forward (DF): In this strategy, the relay decodes the received signal, it generates an estimate of the source message and then re-encodes it and forwards the resulting codeword to the destination. In the case of successful decoding at the relay, the DF strategy performs very well. However, when the relay fails to correctly decode the received signal an error propagation phenomenon is observed. In this case, using the DF strategy is not beneficial. Compress-and-forward (CF): In the compress-and-forward protocol, the relay quantizes the received signal and sends a compressed version of it to the destination. This compression uses the fact that the observations at the relay and the destination are correlated. Indeed, the relay employs source coding considering side information at the destination from the direct transmission. Unlike the DF protocol, CF works well even when the source-to-relay link is not error-free. In [KGG05], it was shown that the achievable rate of DF is higher when the relay is close to the source while CF outperforms DF in terms of achievable rate when the relay gets closer to the destination. In the course of this thesis, we will consider scenarios where the relay is relatively close to the source so that the transmission to the relay is reliable. In such scenarios, DF outperforms other relay strategies [KGG05]. Therefore, in the sequel we restrict ourselves to the DF strategy. In addition to the relaying strategies, the relay can operate in different setups. There exist two setups in relaying: full-duplex relaying and half-duplex relaying. In full-duplex mode, the relay is able to transmit and receive simultaneously while in half-duplex mode the relay cannot transmit and receive at the same time or at the same frequency. Half-duplex relaying is relevant from practical purposes, since it is considered a challenge to provide full-duplex operation at the relay [Poz98], [DL10, p. 324]. In the sequel, we will consider relays that operate in half duplex mode unless otherwise stated Channel Model We consider the relay channel depicted in Figure 3.1. We assume a half duplex relay channel, where the transmission time is divided into two phases. As shown in Figure 3.1, there are three directed transmission links under consideration: the link from the source

67 36 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS to the destination, l sd, the link from the source to the relay, l sr, and the link from the relay to the destination, l rd. We denote by γ sd, γ sr and γ rd the SNR of the source-todestination channel, the source-to-relay channel, and the relay-to-destination channel, respectively. Likewise, we denote by d sd, d sr and d rd the distance from source s to the destination, from source s to the relay, and from the relay to the destination, respectively. Source s encodes its information bits u s into codeword c s of length n s = k/r s bits. We assume that the transmission time is divided into two slots. In the first time slot, source s transmits the modulated sequence x s of codeword c s to both the destination and the relay. This time slot corresponds to the broadcast phase or the relay-receive phase. The relay r receives a noisy version of codeword c s. After processing the received codeword, the relay generates an extra redundancy c r of length n r bits and transmits the modulated version x r to the destination during the second time slot or the relay-transmit phase. In Section 3.1.5, we will describe in more details the information processing at the relay. The channel model can be described by y sr = H sr x s +z sr (3.1) y sd = H sd x s +z sd (3.2) y rd = H rd x r +z rd (3.3) where y sr denotes the received signal at the relay from the source, and y sd and y rd denote the received signal at the destination from the source and the relay, respectively. z sr, z sd and z rd are AWGN noise vectors with zero-mean and variance σ sr, σ sd and σ rd, respectively. H sr, H sd and H rd are diagonal matrices with Rayleigh fading channel coefficients in the main diagonal and zeros everywhere else. We make the assumption that the relay is closer to the source than to the destination. This is a favorable and necessary assumption for decode-and-forward techniques, since it guarantees a low error probability at the relay. The SNRs of the three channels under consideration are linked by γ sr = g sr γ sd, γ rd = g rd γ sd, (3.4) where the gains g sr and g rd are due to shorter transmission distances and are given by g sr = (d sd /d sr ) α and g rd = (d sd /d rd ) α, respectively. As already mentioned in Section 2.1.2, α denotes the path-loss exponent and it is often assumed to be 2 α 6 [Yac93, Rap99]. In the following sections, we first present some information theoretic limits for coding over the relay channel when the DF strategy is used at the relay. Then, we give an overview of the distributed coding schemes for the relay channel.

68 3.1. THE RELAY CHANNEL Achievable Rates of the Relay Channel We consider the decode-and-forward strategy and compute the achievable rate of the relay channel. We assume that the transmission time is divided into two slots. One time slot is allocated to the transmission of the source data and the second time slot to the relay. We define the effective rate of the system as R = k/n with N = n s + n r, where n s and n r have been defined in Section We denote by θ = n s /(n s +n r ) = n s /N (0 θ 1) the parameter which defines the total time allocated to the source s. 1 θ is the total time allocated to the relay. The information data of sources s can be decoded reliably at the destination if the following inequalities hold k n s C(γ sr ) k n s C(γ sd )+n r C(γ rd ). (3.5) where C denotes the channel capacity as defined in Section Dividing by N in both sides of the inequalities, we get R θc(γ sr ) R θc(γ sd )+(1 θ)c(γ rd ). (3.6) The achievable decode-and-forward rate R for the the relay channel is computed according to the max-flow min-cut theorem [FF56]. Here, we briefly recall the max-flow min-cut theorem. This theorem states that in any network, the value of the max flow sent from source node s to sink t is equal to the capacity of the min cut. The min cut is the cut with minimum capacity. Note that a cut is a node partition (S,T) such that s is in S and t is in T. The achievable rate R is given by R = min{θc(γ sr ),θc(γ sd )+(1 θ)c(γ rd )}. (3.7) Achievable Rate in the case of Equal Time Allocation If the time is equally shared between the source and the relay, parameter θ is equal to 1/2 and the achievable rate R is given by { 1 R = min 2 C(γ sr), 1 2 C(γ sd)+ 1 } 2 C(γ rd). (3.8) Figure 3.2 depicts the achievable rate R of the relay channel with respect to the SNR of the source-to-destination channel γ sd. We set the path-loss exponent α to 3.52 and we consider a distance ratio d sr /d sd = 1/4. Under the condition that the relay is closer to the source than to the destination, i.e., C(γ sd ) < C(γ sr ) and assuming an

69 38 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS 8 6 Point-to-Point Com. Relay Channel bits/use γsd [db] Figure 3.2 Achievable rate over the relay channel with equal time allocation, d sr /d sd = 1/4 and Gaussian input variables. equal time allocation between the source and the relay, i.e., θ = 1/2, the achievable rate R is given by R = 1 2 C(γ sd)+ 1 2 C(γ rd). (3.9) For comparison, we consider the rate of the point-to-point communication over an AWGN channel. Higher rates are achieved by cooperating through the relay. For instance, let us consider an example with SNRs γ sd = 1 (0 db), γ sr = (21.2 db) and γ sr = 2.75 (4.4 db). These SNRs are obtained if the relay is on a line between the source and the destination with d sr /d sd = 1/4 and a path-loss exponent α = The achievable rate R with Gaussian input variables in bits per channel use for the point-to-point transmission without relay is given by R = C(γ sd = 1) = 1 bits per channel use. (3.10) The achievable rate R for the relay channel with equal time sharing (θ = 1/2) according to (3.8) is given by { 1 R = min 2 C(γ sr = ), 1 2 C(γ sd = 1)+ 1 } 2 C(γ rd = 2.75) (3.11) = 1.45 bits per channel use. Compared to direct transmission, communication with the help of the relay allows the rate to be increased from 1 to 1.45 bits per channel use Achievable Rate in the case of Optimal Time Allocation Depending on the quality of the channels in the relay network, θ can be optimally allocated in order to achieve higher rates. In particular, parameter θ can be optimized

70 3.1. THE RELAY CHANNEL 39 such that the rate R is maximized: θ = argmaxr (3.12) θ As shown in [HH06], a closed form expression of the optimal time allocation parameter θ can be found under the assumption C(γ sd ) C(γ rd ). It follows that θc(γ sd )+(1 θ)c(γ rd ) is monotone decreasing with θ for C(γ sd ) C(γ rd ) and θc(γ sr ) is monotone increasing with θ. The solution of the maximization is found at the cross-over point of θc(γ sd )+(1 θ)c(γ rd ) and θc(γ sr ) and θ is computed by solving the equation Solving (3.13) gives θ C(γ sd )+(1 θ )C(γ rd ) = θ C(γ sr ). (3.13) θ = Therefore, the achievable rate R is given by R = C(γ rd ) C(γ sr )+C(γ rd ) C(γ sd ). (3.14) Achievable Rate and Relay Position C(γ rd )C(γ sr ) C(γ sr )+C(γ rd ) C(γ sd ). (3.15) As shown in Section , the optimal achievable rate can be derived as a function of the SNRs of the different links in the relay network. According to Section 3.1.1, these SNRs are linked by (3.4). Therefore, the achievable rate can be written as a function of γ sd and d sr /d sd. In Figure 3.3, we plot the achievable rate obtained according to (3.15) with respect to γ sd and the relay position d sr /d sd. The path-loss exponent α is assumed to be From Figure 3.3, we observe that the achievable rate reaches its peak value when the relay is positioned at half distance between the source and the destination. With increasing γ sd, the achievable rate depends less on the position of the relay (flatter curves are observed for high γ sd ) Outage Probability In this section, we study the outage behavior of the relay channel. This analysis is relevant for channels that exhibit block fading. An outage event is declared if the source data is not decoded reliably at the destination. We denote by e out the outage event, and by ē out its complement. The information data of source s can be reliably decoded at the destination if the values of the fading coefficients h sd, h sr, and h rd are such that the inequalities (3.5) hold. Furthermore, reliable decoding of the source data is also achieved if the direct transmission from s to the destination is not in outage, i.e., if the following inequality holds k n s C(γ sd ). (3.16)

71 40 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS R d sr /d sd γ sd [db] 5 10 Figure 3.3 The achievable rate plotted as a function of γ sd and the relay position d sr /d sd : the peak value is reached for d sr /d sd = 1/2 for low SNRs. For high SNRs, flatter curves are observed. BPSK modulation is considered. Hence, the destination can decode successfully if either (3.5) or (3.16) hold. The event ē out can then be written as ē out = (k n s C(γ sr ) k n s C(γ sd )+n r C(rd)) (k n s C(γ sd )). (3.17) In Figure 3.4, we plot the outage probability over a Rayleigh block fading channel with BPSK modulation for rate R = 1/3. The solid curve represents the outage probability for the relay channel and the dashed curve accounts for the direct transmission. We assume that d sr = (1/4)d sd and d rd = (3/4)d sd. The communication system with relay can achieve better performance than the system without relay. For instance, at FER 10 2, a gain of almost 10.2 db can be achieved with respect to non-cooperation. From Figure 3.4, in addition to the coding gain achieved by relaying, we observe a diversity gain with respect to the the non cooperative case. This gain is translated by a change in the slope of the curve corresponding to the relay network Distributed Codes for the Relay Channel As explained in Sections and 3.1.4, cooperation through relay improves capacity and provides transmit diversity by adding an extra space dimension. In order to harvest the gains predicted by information theory, practical cooperation schemes have been recently proposed for the relay channel. In [Lan02] and [HN02], relay coding was addressed. In [Lan02], repetition codes were used at the relay and maximum ratio com-

72 3.1. THE RELAY CHANNEL Relay Channel R=1/3 Point-to-point Com. R=1/3 Outage rate γ sd [db] Figure 3.4 Outage probability for BPSK modulation for a rate R = 1/3 over Rayleigh block fading channel. bining (MRC) was performed at the destination and in [HN02] distributed rate compatible codes were proposed. Since cooperative communication involves two component codes, turbo-like codes are a natural fit for the relay channel. Distributed turbo coding was first introduced in [VZ03], and later other coding schemes [SV05, Tho08, STS09] were proposed for the relay channel. In these schemes, known coding structures as PCCs and SCCs are used in a distributed manner between the source and the relay. In the following, we first review the distributed parallel concatenated codes (DPCCs) and then we describe the distributed serially concatenated codes (DSCCs) Distributed Parallel Concatenated Codes DPCCs were first introduced in [VZ03]. Figure 3.5 shows the block diagram of the DPCC for the relay channel. The transmission time is divided into two slots. In the firstphase,thesourceencodesitsinformationu s intocodewordc s byanencoderc 1 and broadcasts the coded bits to both the relay and the destination. During this slot, the relay decodes the received signals and generates an estimate û of the source message. It then interleaves û s into û s and re-encodes it by an encoder C 2 prior to forwarding. In the second slot, the relay forwards its own parity to the destination. The destination receives two encoded copies of the original message and jointly decodes them by an iterative decoding algorithm in the same way as for a conventional PCC. The proposed technique achieves a combined diversity and coding gain.

73 42 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS Source Encoder Decoder Encoder Relay Figure 3.5 Block diagram of the DPCC. In [VZ03], error free source-relay link was assumed. More recent works have considered the relay channel with non ideal channel between the source and the relay [SV05, Tho08]. Soft decoding and soft re-encoding at the relay were proposed in[sv05]. According to this strategy, the relay performs a soft decoding of the received signal and re-encodes it softly using a SISO encoder algorithm which has some similarities to the SISO decoding algorithm. This novel technique shows performance that outperforms the classic DF strategy. Another work presented in [Tho08] considers the noisy relay channel. In [Tho08], the authors present a technique used at the decoder in order to mitigate the effect of errors at the relay. Based on the assumption of memoryless channel, the information bit u s and its estimate û s are linked by Pr(u s û s ) = p. During the decoding process, the LLRs L(û s ) relative to the noisy estimates û are converted into the LLRs L(u s ) relative to the actual information bit u s and vice versa by the following transfer function F p ( ) (1 p)exp(+lin /2)+pexp( L in /2) L out = F p (L in ) = log (3.18) pexp(+l in /2)+(1 p)exp( L in /2) Figure 3.6 shows simulation results of a rate-1/3 distributed PCC. The source uses the 4-state, rate-1/2, recursive convolutional encoder with generator polynomials (1,5/7) 8. The relay encodes using the same encoder but it forwards only the parity bits. Hence the global rate of the overall system is R = 1/3. We first consider a case where reliable transmission is achieved at the relay. We assume a relative source-torelay distance d sr /d sd = 1/4, which translates into g sr = (21.2 db) and g rd = 2.75 (4.4 db), respectively. We consider a block length k = 1504 bits. For comparison purposes, we also consider the non-cooperative scenario. For fair comparison, we plot the performance assuming that the source transmits with a rate 1/3 which corresponds to the effective rate of the overall system with relay. Figure 3.6 shows the significant gain achieved by the cooperative system with respect to direct transmission. For instance, for BER = 10 3, a gain of 5 db is achieved by the distributed coding. In Figure 3.6, γ b min = 2.2 db corresponds to the minimum value of the SNR that achieves an overall rate R eff = 1/3. γ b min is obtained from (3.7) with θ = 2/3. The system performs within almost 2 db from capacity.

74 3.1. THE RELAY CHANNEL Point-to-Point Com. R=1/3 DPCCC R=1/ BER 10-3 γ b min =-2.2 db γ b sd[db] Figure 3.6 Simulation results over AWGN channel ; d sr /d sd = 1/4; k = 1504 bits Point-to-Point Com. R=1/3 DF DF with F p at the decoder 10-2 BER ,5-1 -0,5 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 6 γ b sd[db] Figure 3.7 Simulation results over AWGN channel ; d sr /d sd = 3/4; k = 1504 bits. BER performance comparison between the classic DF and the use of F p at the decoders We also consider the case where the relay is closer to the destination than to the

75 44 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS Source Encoder Decoder Encoder Relay Figure 3.8 Block diagram of the DSCC. source, i.e, the source-to-relay link is not strong enough and errors occur at the relay. We assume a relative source-to-relay distance d sr /d sd = 3/4, which translate into g sr = 2.75 (4.4 db) and g rd = (21.2 db), respectively. In Figure 3.7, we plot the performance of the DPCC using the classic decode-and-forward at the relay, and the performance of the system using the approach in [Tho08]. As shown in Figure 3.7, the use of function F p atthedecodersimprovestheperformanceofthesystemespeciallyatverylowsnrs. For low γ b sd, γb sr is relatively low (γ sr = g sr γ sd ) and the BER at the relay is relatively high while with increasing γ b sd, γb sr also increases and few errors occur at the relay. Therefore, the impact of F p is observed at very low SNR γ b sd Distributed Serially Concatenated Codes DSCCs for the relay channel were first addressed in [STS09]. Figure 3.8 shows the block diagram of a DSCC. The relay decodes the received signal from the source and generatesanestimateĉ s oncodewordc s.theestimatedcodewordĉ s istheninterleaved and re-encoded prior to forwarding. The overall network is viewed as an SCC. As in[tho08], the authors in[sts09] consider the relay channel with a noisy sourcerelay link and use the same approach to limit the error propagation phenomenon. Once again, a memoryless channel is assumed and therefore the codewords c s and their estimates ĉ s are linked by Pr(c s ĉ s ) = p. During the exchange of extrinsic information, the LLR L(ĉ s ) of the noisy estimate ĉ s is converted into the LLR L(c s ) of the actual codeword bit c s and vice versa by the transfer function F p given in (3.18). The decoding at the destination is performed using a decoding strategy that resembles the decoding of an SCC. DSCCs achieve improved error floor performance with respect to DPCCs while DPCCs perform better in the waterfall region. 3.2 The Multiple-Access Relay Channel From the simplest scheme of cooperation, i.e., the relay channel, we now consider the MARC. The MARC is a model for network topologies where multiple sources

76 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL 45 r d Figure user MARC: sources s 1 and s 2 transmit to a single destination with the help of a relay. communicate with a single destination with the help of a relay node. The intermediate relay node aids communication between the sources and the destination. The MARC was first investigated in [KvW00] where an outer bound on the capacity region was derived using cut-sets. The authors also presented an achievable rate region for the Gaussian MARC which was extended in [KvW04] using block Markov encoding and backward decoding. Tighter outer bounds on the capacity of the discrete memoryless MARC were presented in [SKM04a] taking into account the causal relationship between the source and relay inputs. In this section, we consider the two-user MARC, where two sources communicate with one sink with the help of one relay. Figure 3.9 depicts the MARC under consideration. This system can be used for the cooperative uplink for two mobile stations to a base station with the help of a relay. Here, we consider channels with time-division access. Hence, the first source broadcasts to the relay and the destination in the first time slot. The second source broadcasts to the relay and the destination in the second time slot, and the relay transmits orthogonally to the destination in the third time slot. Source s 1 and source s 2 transmit their own codewords x 1 of length n 1 = k 1 /R 1 and x 2 of length n 2 = k 2 /R 2, respectively. k 1 and k 2 denote the information length for sources s 1 and s 2, respectively, and R 1 and R 2 the code rate for sources s 1 and s 2, respectively. Since we consider an orthogonal scenario, the relay receives a noisy version of x 1 and x 2 separately. The relay possesses information about source s 1 and source s 2 messages. If the relay chooses to transmit redundancy about the information of only one source, it requires an additional time slot to act as a relay for both sources. Therefore, in order to achieve a higher throughput, the relay may combine the information it possesses about the two sources messages and will then transmit an additional redundancy x r of length n r to the destination. This additional redundancy contains information about the messages of both sources s 1 and s 2. In [HSOB05, YK07], this combination consists of a simple XOR and is termed as network coding. The received signals at the destination and the

77 46 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS relay are respectively given by y si d = H si dx i +z si d i = 1,2 (3.19) y si r = H si rx i +z si r i = 1,2 (3.20) y rd = H rd x r +z rd (3.21) where the definitions of H si d, H si r, H rd,z si d, z si r and z rd remain the same as in Section 3.1. Again, we make the assumption that the relay is closer to the sources than to the destination. Moreover, we assume for simplicity that both sources are at the same distance from the relay and from the destination, i.e., γ si d = γ sd and γ si r = γ sr. Thus, the SNRs of the considered MARC are linked as in (3.4). In the following sections, we present the achievable rate of the 2-users MARC and then we summarize the work in[hsob05, YK07] which considers joint channel network coding for the MARC Achievable Rates for the MARC In this section we compute the achievable rates for the MARC of Figure 3.9, following the approach proposed in [Hau08]. In [Hau08] the authors considered the achievable decode-and-forward rate of a 2-user system assuming the time division MARC model with optimized allocation of the transmission time. Let k i, n i, i = 1,2, n r be as defined in Section 3.2. We define the rate for source s i as R i = k i /N for i = 1,2. We also define K = k 1 + k 2, N = n 1 + n 2 + n r. From these definitions it follows that the rate of the overall system is R eff = R 1 + R 2 = k 1 +k 2 /(n 1 +n 2 +n r ) = K/N. The information data of sources s 1 and s 2 can be decoded reliably at the destination if the following inequalities hold [Hau08]: k 1 n 1 C(γ s1 r) k 2 n 2 C(γ s2 r) k 1 n 1 C(γ s1 d)+n r C(γ rd ) k 2 n 2 C(γ s2 d)+n r C(γ rd ) k 1 +k 2 n 1 C(γ s1 d)+n 2 C(γ s2 d)+n r C(γ rd ). (3.22) We define the time allocated to s 1, s 2 and to the relay as θ 1 = n 1 /N, θ 2 = n 2 /N and θ r = N r /N, respectively. Notice that θ 1 + θ 2 + θ r = 1. Dividing by N in both sides of the inequalities in (3.23), we have R 1 θ 1 C(γ s1 r) R 2 θ 2 C(γ s2 r) R 1 θ 1 C(γ s1 d)+θ r C(γ rd ) R 2 θ 2 C(γ s2 d)+θ r C(γ rd ) R 1 +R 2 θ 1 C(γ s1 d)+θ 2 C(γ s2 d)+θ r C(γ rd ). (3.23)

78 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL 47 Denotebyσ = R 2/R 1 theratiobetweentheratesofsources 2 ands 1.Ifasymmetric MARC is considered, σ = 1. From (3.23) and according to the max-flow min-cut theorem, the achievable rate R 1 is given by R 1 = min{θ 1 C(γ s1 r),θ 2 C(γ s2 r)/σ, θ 1 C(γ s1 d)+(1 θ 1 θ 2 )C(γ rd ), (θ 2 C(γ s2 d)+(1 θ 1 θ 2 )C(γ rd ))/σ, (θ 1 C(γ s1 d)+θ 2 C(γ s2 d)+(1 θ 1 θ 2 )C(γ rd ))/(1+σ)}. (3.24) Achievable Rate with Equal Time Allocation We first consider equal time allocation for the two sources and the relay, i.e, θ i = θ r = 1/3,i = 1,2. We also assume a symmetric MARC, i.e., σ = 1, γ s1 r = γ s2 r and γ s1 d = γ s2 d. The achievable rates R 1 and R 2 are given by { 1 R 1 = R 2 = min 3 C(γ sr), 1 3 C(γ sd)+ 1 } 6 C(γ rd). (3.25) Let us consider as in Section the SNRs γ sd = 1 (0 db), γ sr = (21.2 db) and γ rd = 2.75 (4.4 db). The achievable rates R 1 and R 2 for direct transmission without relay with equal time allocation (θ 1 = θ 2 = 1/2) are R 1 = R 2 = θ 1 C(γ sd = 1) = θ 2 C(γ sd = 1) = 1 2 C(γ sd = 1) = 0.5 bits per channel use. For communication with relay, the achievable rates are given by { 1 R 1 = R 2 = min 3 C(γ sr = ), 1 3 C(γ sd = 1)+ 1 } 6 C(γ rd = 2.75) = 0.65 bits per channel use. (3.26) (3.27) Thanks to the relay, the rate is increased from 0.5 bits per channel use to 0.65 bits per channel use Achievable Rate with Optimal Time Allocation Parameter θ can be optimized in order to achieve higher rates. For a 2-user relay network, the optimal time allocation can be derived so that R 1 is maximized, subject to some ratio σ = R 1/R 2 between the achievable rates R 1 and R 2 for user one and two, respectively, is satisfied [Hau08]: [θ opt 1,θ opt 2 ] = argmaxr 1 subject to σ = R 2/R 1 and θ r = 1 θ 1 θ 2. (3.28) [θ 1,θ 2 ] If conditions C(γ s1 d) < C(γ rd ), C(γ s2 d) < C(γ rd ), C(γ s1 d) < C(γ s1 r) and C(γ s2 d) < C(γ s2 r) hold, a closed-form expression for the optimal time allocation can be derived

79 48 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS 8 Equal time allocation Optimal time allocation 6 bits/use γsd [db] Figure 3.10 Achievable sum rate for the 2-users MARC for both equal and optimal time allocation over AWGN channel and Gaussian input variables. [Hau08], θ opt 1 = C(γ rd ) (1+σα)C(γ rd )+(1+σ)C(γ s1 r) C(γ s1 d) σαc(γ s2 d) (3.29) and where α = C(γ s1 r)/c(γ s2 r). The achievable rates R 1 and R 2 are then given by θ opt 2 = θ opt 1 σα, (3.30) R 1 = C(γ s1 r)c(γ rd ) (1+σα)C(γ rd )+(1+σ)C(γ s1 r) C(γ s1 d) σαc(γ s2 d) (3.31) and R 2 = σr 1. (3.32) Again, we consider a symmetric MARC (σ = 1), γ s1 r = γ s2 r and γ s1 d = γ s2 d from which it follows α = 1. We obtain and θ opt 1 = θ opt 2 = 1 2 C(γ rd ) C(γ rd )+C(γ sr ) C(γ sd ) (3.33) R 1 = R 2 = 1 C(γ sr )C(γ rd ) 2C(γ rd )+C(γ sr ) C(γ sd ). (3.34) The sum rate of the overall system (effective rate) R eff is given by R eff = R 1 +R 2 = C(γ sr )C(γ rd ) C(γ rd )+C(γ sr ) C(γ sd ). (3.35)

80 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL 49 From (3.35), we observe that the MARC achieves the same sum capacity as the relay channel and therefore the optimization problem can be treated as a capacity optimization problem for a single user relay channel [Hau08]. Figure 3.10 shows the achievable sum rates of the 2-user AWGN MARC for both equal and optimal time allocation. The curves of the achievable rates are plotted for BPSK modulation, d sr /d sd = 1/4 and a path-loss exponent α = As shown in Figure 3.10, a higher rate can be achieved with optimal time allocation between the sources and the relay. For instance, for γ sd = 6 db, a sum rate R eff = 0.47 bits per channel use is achieved when equal time allocation is considered while a sum rate R eff = 0.7 bits per channel use is obtained for optimal time allocation Outage Probability for the MARC We consider the outage behavior of the 2-user MARC depicted in Figure 3.9. An outage event is declared if the data of at least one source is not decoded reliably at the destination.onceagain,wedenotebye out theoutageevent,andbyē out itscomplement. The information data of sources s 1 and s 2 can be reliably decoded at the destination if the values of the fading coefficients h s1 d, h s2 d, h s1 r, h s2 r and h rd are such that the inequalities in (3.23) hold. Furthermore, reliable decoding of the information data of s 1 and s 2 is also achieved if the direct transmissions from s 1 and s 2 to the destination are not in outage, i.e., if the following two inequalities hold k 1 n 1 C(γ s1 d), k 2 n 2 C(γ s2 d). (3.36) Hence, the destination can decode successfully if either (3.23) or (3.36) hold. The event ē out can then be written as ē out = (k 1 n 1 C(γ s1 r) k 2 n 2 C(γ s2 r) k 1 n 1 C(γ s1 d)+n r C(γ rd ) k 2 n 2 C(γ s2 d)+n r C(γ rd ) k 1 +k 2 n 1 C(γ s1 d)+n 2 C(γ s2 d)+n r C(γ rd )) (k 1 n 1 C(γ s1 d) k 2 n 2 C(γ s2 d)). (3.37) Figure 3.11 shows the outage rate of the 2-user MARC. For comparison with the direct transmission, we consider two point-to-point channels over which two sources s 1 and s 2 transmit to a destination. For this, we define the outage event e out as for the MARC, i.e., an outage is declared if the data of at least one source is not decoded reliably at the destination. Therefore, the event ē out is given by the following equation ē out = k 1 n 1 C(γ s1 d) k 2 n 2 C(γ s2 d). (3.38)

81 50 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS 10 0 No cooperation MARC 10-1 Outage probability γsd [db] Figure 3.11 Outage probabilty for a rate R = 1/3 with BPSK modulation over the 2-user MARC and for the non-cooperative transmission. AWGN channels are considered. In the example, we consider a rate R = 1/3 and equal time allocation between the 2 sources and the relay (θ 1 = θ 2 = θ r = 1/3). The outage probability is plotted for constrained input variables (in particular, for BPSK modulation) and for a relative source-to-relay distance d sr /d sd = 1/4. We can observe in Figure 3.11 that the system for the MARC achieves, in addition to the coding gain, a better diversity than the non-cooperative system Joint Channel-Network Coding for the Multiple-Access Relay Channel As explained in Section 2.7, network coding is a novel data processing technique that exploits the characteristics of the wireless medium in order to increase the capacity or the throughput of the network. Some recent works [HSOB05, HD06, YK07] proposed a joint channel-network coding design. In the following, we summarize the proposed coding strategies for the MARC of [HD06] and [YK07]. In [HD06], a fundamental assumption is that the relay decodes the message reliably while in [YK07] the authors consider the case when the transmission to the relay is not recovered perfectly. For this aim, we present the approaches in two sections: the first section considers errorfree source-to-relay links and describes the approach of [HD06] and the second section

82 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL 51 Encoder Decoder Encoder Punc Decoder Encoder Figure 3.12 Block diagram of the joint network/channel coding scheme proposed in [HD06]. considers source-to-relay channels with noise and describes the approach of [YK07] Encoding Scheme for Reliable Source-to-Relay Transmission Figure 3.12 illustrates the block diagram of the coding scheme proposed in [HD06] for the MARC. The information sequences u 1 of length k 1 and u 2 of length k 2 of source s 1 and s 2, respectively, are protected against transmission errors with channel codes C 1 and C 2 which output the blocks c 1 of length n 1 and c 2 of length n 2, respectively. c 1 and c 2 are then modulated into x 1 and x 2, respectively. The transmission time is divided into three slots. In the first time slot, source s 1 broadcasts its codeword x 1 to both the relay and the destination. In the second time slot, source s 2 transmits its codeword x 2 to the relay and the destination. The relay decodes the received codewords and generates hard estimates û 1 and û 2 about u 1 and u 2, respectively. The estimates û 1 and û 2 are then interleaved by interleavers Π 1 and Π 2, encoded by a channel code C r and punctured by a puncturer into codeword c r of length n r. In the third time slot, the relay forwards x r, the modulated version of codeword c r, to the destination. Based on the three observations y s1 d, y s2 d and y rd, an iterative decoding is performed at the destination exploiting the additional redundancy provided by the relay. As depicted in Figure 3.13, there are three SISO decoders. Decoders C1 1 and C2 1 correspond to the channel encoders C 1 and C 2 at s 1 and s 2, respectively. Decoder Cr 1 corresponds to the encoder at the relay. First, decoders C1 1 and C2 1 calculate a posteriori LLRs L(u 1 ) and L(u 2 ) using the channel LLRs L ch (c 1 ) and L ch (c 2 ), respectively. Initially, no a priori information is available (L a,c 1 (u 1) = 0 and L 1 a,c 1 (u 2) = 0) at 2 decoders C1 1 and C2 1, respectively. The SISO decoder Cr 1 calculates a posteriori LLRs L (u 1 ) and L (u 2 ) based on the relay-to-destination channel LLR L ch (c r ) and on a pri-

83 52 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS Decoder - Decoder Decoder Figure 3.13 Iterative decoding at the destination. ori information L a,c 1(u r 1 ) and L a,c 1(u r 2 ) about u 1 and u 2, respectively, from the other two SISO decoders. In order to obtain the required a priori information, the extrinsic information L e,c 1 (u 1) = L(u 1 ) L 1 a,c 1 (u 1) and L 1 e,c 1 (u 2) = L(u 2 ) L 2 a,c 1 (u 2) has 2 to be interleaved and mixed in the same way as it is done at the relay. Then, extrinsic information L e,c 1(u r 1 ) = L (u 1 ) L a,c 1(u r 1 ) and L e,c 1(u r 2 ) = L (u 2 ) L a,c 1(u r 2 ) are passed back to decoders C1 1 and C2 1 where it can be exploited as a priori information in the next decoding round. After several iterations, decoder Cr 1 outputs the hard estimates û 1 and û 2. With this system, significant coding gains have been reported with respect to noncooperation. Moreover, it allows to efficiently exploit the redundancy transmitted by the relay. In this scheme, the links between the sources and the relay are assumed to be good enough so that no errors occurs at the relay. Meanwhile, a more recent work [YK07] considered a noisy relay scenario where soft processing is performed at the relay. In the following section, we describe in details the proposed system Noisy Source-to-Relay Channel Joint network/channel coding for the MARC was also investigated in [YK07]. The authors proposed a distributed encoding scheme which, unlike the approach in [HD06], performs well even when the transmission to the relay cannot be recovered perfectly. At the sources, the same operations are performed as for the system described in Section The difference with respect to the last system is the encoding strategy at the relay. Figure 3.14 illustrates the block diagram of the system proposed in [YK07]. The relay node operation is described by the following steps: the relay decodes the received message from both sources and derives soft estimates L(c 1 ) and L(c 2 ) about codewords c 1 and c 2, respectively. The relay permutes the LLRs L(c 2 ) of codeword from s 2 into L( c 2 ) and then calculates the LLR L r of the network coded message by ( ) exp(l(c1 ))+exp(l( c 2 )) L r = log (3.39) 1+exp(L(c 1 )+L( c 2 ))

84 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL 53 Encoder Decoder Decoder Encoder Figure 3.14 Block diagram of the joint network coding scheme for noisy relay proposed in [YK07]. Decoder Decoder Figure 3.15 Iterative decoding at the destination. At the destination, an iterative decoding algorithm is performed based on the three observations from the two sources and the relay. Figure 3.15 depicts the iterative message passing between the two decoders C1 1 and C2 1. We provide in the next section a study on how to process information at the relay. We explain how the soft LLR is transmitted at the relay and we compare that with the case where the relay forwards the hard combination of the messages How to Process the Information at the Relay? The proposed scheme in [YK07] is based on soft decoding at the relay. As described in the previous section, the relay computes the LLR of the combined codeword using equation (3.39) and transmits it to the destination. Transmitting this analog value requires practical consideration. The question is: is it always beneficial to transmit the soft value? Can the relay simply transmit the binary combination of the estimated codewords? To answer this question, we have studied the same scenario under different channel

85 54 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS The Soft case The Hard case 10-2 γ b rd= 5 db γ b rd=-5 db γ b rd=0 db γ b rd=-10 db BER 10-3 γ b rd= 10 db γ b sd [db] Figure 3.16 BER curves over AWGN channel for both soft case (red curves) and hard case (blue curves). γsr b = 5 db and different values of γrd b are considered = 10, 5,0,5,10 db). (γ b rd conditions (channels with different SNRs). We have considered two cases. In the first case, the relay operates as described in [YK07]. We call this case the soft case. In the second case, the relay decodes the received signals from both sources, generates estimates ĉ 1 and ĉ 2 on codewords c 1 and c 2, respectively, and then combines by a simple XOR ĉ 1 with the interleaved version of ĉ 2 and transmits the resulting codeword to the destination. We call this case the hard case. We consider two fixed SNR values for the source-to-relay channel: γsr b = 5 db which corresponds to a relatively strong link between the sources and the relay, and γsr b = 0 db which means that the link between the sources and the relay is poor. For the relayto-destination channel, we consider different SNR values γrd b = 10 db, γb rd = 5 db, γrd b = 0 db, γb rd = 5 db and γb rd = 10 db. Figure 3.16 and Figure 3.17 show the simulations results for γsr b fixed to 5 db and 0 db. From Figure 3.16 we observe that for high source-to-relay SNR better performance is obtained when the relay simply performs hard decisions. On the other hand, Figure 3.17 shows that processing soft information at the relay node yields better performance for low source-to-relay SNR. These results are intuitively expected, in the sense that if the relay possesses the right information there is no need to process this information, it can simply performs hard decisions. In order to complete our analysis, we have modeled the source-to-relay-todestination channel for both cases. It was shown in [WCGL07] that these links can

86 3.2. THE MULTIPLE-ACCESS RELAY CHANNEL γ b rd= 5 db γ b rd= 10 db γ b rd= 0 db γ b rd= 5 db γ b rd= 10 db BER The Soft case The Hard case γ b sd [db] Figure 3.17 BER curves over AWGN channel for both soft case (red curves) and hard case (blue curves). γsr b = 0 db and different values of γrd b are considered = 0,5,10 db). (γ b rd be modeled by a virtual memoryless channel with an equivalent SNR γ b eq. The soft case: To compute the equivalent SNR of the source-to-relay-to-destination channel, we make the assumption that the LLRs at the output of the SISO decoder at the relay have the same form as the output of an AWGN channel with BPSK modulation. L(x) = Pr(x = 1 y sr) Pr(x = 1 y sr ) = µ L(x+n L ) (3.40) where n L is a zero-mean white Gaussian noise with variance σl 2. The LLRs are Gaussian distributed with mean µ L and variance σ 2 = µ 2 L σ2 L. The mean µ L and the variance σ 2 are computed empirically. Before forwarding, the LLRs obtained at the output of the decoder are normalized by µ L and multiplied by a factor β [SV05]. β is computed in order to normalize the transmitted energy averaged over the realizations of the source-to-relay channel and is given by β = E s E[σ 2 x +σ 2 L ] = The received signal at the destination is then given by 1. (3.41) 1+σL 2 y rd = β(x+n L )+n rd (3.42)

87 56 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS γrd b γrd b γrd b γrd b γrd b Table 3.1 Equivalent signal to noise ratio γeq b of the virtual source-to-relay-to-destination channel. The Hard case The Soft case µ eq σ eq γeq b µ eq σ eq γeq b = 10 db db db = 5 db db db = 0 db db db = 5 db db db = 10 db db db The equivalent variance of the virtual source-to-relay-to-destination channel is given by σeq 2 σ 2 = µ 2 +σ2 L +σ2 rd (3.43) and the mean µ eq is equal to β. The hard case: In this case the relay decodes the received signals from both sources to obtain estimates ĉ 1 and ĉ 2. Then it forms c r as The received signal at the destination is given by x r is the modulated version of c r. c r = ĉ 1 π(ĉ 2 ) (3.44) y rd = x r +n rd (3.45) The virtual channel is modeled as an AWGN channel with mean µ eq and the variance σ 2 eq which can be computed numerically. Forbothcases,wecomputetheequivalentSNRγ b eq = µ 2 eq/σ 2 eq oftheresultingvirtual channel. The values of γ b eq are given in Table 3.1. Results in Table 3.1 are in agreement with the simulation results: for high source-to-relay SNR, the equivalent SNR of the modeled channel is higher when the relay makes hard decision than when transmitting soft information, while it is lower for lower source-to-relay SNR. Numerical results in Figure 3.16 and Figure 3.17 as well as the results in Table 3.1 lead us to the conclusion that in scenarios when DF is used at the relay, processing with soft information does not improve performance with respect to decode and add hard decisions unless the relay is far away from the source. For instance, when the BER at the relay is around 0.08 which corresponds relatively to a high error rate, sending the LLRs as done in [YK07] is the best choice while for a BER around processing with hard decision at the relay is more appropriate. Since we are dealing with AWGN channels, poor source-to-relay links correspond to a relay position far from the sources and relatively strong source-to-relay links correspond to a relay position close to the sources.

88 3.3. CODED COOPERATION IN A TWO-USER SCENARIO 57 Figure 3.18 Two-user cooperation: Each source acts as a relay for its partner. X X X X Figure 3.19 The four possible cases of cooperation depending whether each source decodes successfully or not its partner information. 3.3 Coded Cooperation in a Two-User Scenario Two-User Cooperation Another form of cooperation is the two-user network [NHH04, JHHN04], where each user transmits not only its own information, but also some version of the partner information, acting therefore as a relay. This user cooperation methodology is called coded cooperation. The network is depicted in Figure Two sources s 1 and s 2 cooperate to communicate statistically independent data to a single destination d. At a first time, we consider TDMA. Each source provides k information bits, it encodes them into codeword of length n 1 bits and broadcasts it to the destination and to the partner. Each source thus receives a noisy version of the coded message from its partner.if a source can correctly decode the partner message, it computes and transmits n 2 additional parity bits for the partner message. If a source cannot correctly decode its partner data, n 2 additional parity bits for the source own data are transmitted to the destination. Therefore, the overall rate for each user is R = k/(n 1 + n 2 ) = k/n, where n = n 1 + n 2. Indeed, if successful decoding occurs at the partner node, the codeword of each source is partitioned into two sets: one partition (n 1 ) transmitted by the source itself and the other partition (n 2 ) by the partner. According to this, we can distinguish four different cooperative

89 58 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS cases illustrated in Figure In Case 1, decoding at nodes s 1 and s 2 is successful resulting in the fully cooperative scenario. In Case 2, decoding at node s 2 is successful, decoding at node s 1 fails. Consequently, none of the users transmits the second set of code bits for s 2 in the second frame, s 1 and s 2 transmit the second set for s 1. The two independent copies of s 1 bits are optimally combined at the destination. Case 3 is similar to Case 2 with reversed roles of s 1 and s 2. In Case 4, decoding at nodes s 1 and s 2 fails and the system reverts to the non-cooperative transmission. It is obvious that the destination must know which of these cases has occurred in order to decode the received bits. Naturally, the application of turbo codes is investigated in coded cooperation since coded cooperation involves two code components [JHHN04]. This coded cooperation as shown in [NHH04, JHHN04] achieves diversity and noticeable gain over non-cooperative networks. Recently, a network coding approach was proposed in[xfkc07] for this cooperative scenario. Since both cooperative communication and network coding intend to improve the network performance, combining them is promising. In the following section, we will summarize the coding approach proposed in [XFKC07] and we will extend it to a non-orthogonal scenario where the sources are allowed to transmit simultaneously Network Coding in Orthogonal Two-User Cooperative Scenario The scenario under consideration is the same as the scenario depicted in Figure In [XFKC07], all channels are assumed to be orthogonal and orthogonality is obtained via TDMA. Sources s 1 and s 2 cooperate to deliver their k information bits to the common destination d. During time slot t, source s 1 transmits in the first half slot and source s 2 transmits in the second half slot. Sources s 1 and s 2 encode their information bits u 1 and u 2 into their codewords c 1 and c 2, respectively. The code generator matrix for the locally generated information bits being G L, c 1 and c 2 are given by c 1 = u 1 G L c 2 = u 2 G L. (3.46) After receiving the frame sent by its partner, each source attempts to decode its partner information. If decoding succeeds, then each source transmits the XOR combination of the codeword containing its own information and the codeword containing the partner information. Note that the codeword containing the partner information is obtained by interleaving the decoded information bits u 1 and u 2 into ũ 1 and ũ 2, respectively, by interleaver π and re-encoding them by a different or the same encoder used at the source into codewords c 2 and c 1, respectively. The code generator matrix for the relayed bits being G R, c 2 and c 1 are given by c 1 = ũ 2 G R c 2 = ũ 1 G R. (3.47)

90 3.3. CODED COOPERATION IN A TWO-USER SCENARIO 59 Table 3.2 Transmission time for two time slots (four successive half slots) t 1 t 2 t 3 t 4 d c 1 1 c 2 2 c 2 2 c 1 3 c 3 1 c 2 4 c 4 2 s 2 c 1 1 Tx c 1 3 c 3 1 Tx s 1 Tx c 2 2 c 2 2 Tx c 2 4 c 4 2 If a source fails to correctly decode its partner information, it operates in a noncooperative mode and transmits only its own codeword. Without loss of generality, we will consider the encoding at source s 1. Encoding at source s 1 During time slot t source s 1 must convey its local information u 1 (t) and relay source s 2 information assuming it has decoded u 2 (t 1) correctly. The transmitted codeword is the XOR of the codeword containing source s 1 local information and source s 2 relayed information w 1 (t) = c 1 (t) c 1(t) = u 1 (t)g L π(u 2 (t 1))G R = [u 1 (t) ũ 2 (t 1)] [ G L G R ] (3.48) Taking the XOR of two codewords is[ equivalent ] to encoding u 1 (t) and ũ 2 (t 1) using a nested code with generator G = then encodes only its local information. G L G R c 1 = u 1 G L =. If source s 1 fails to decode u 2 (t 1), it [ ] [ G L u 1 (t) 0 G R ] (3.49) In Table 3.2, we illustrate the transmission time for two time slots, i.e., four successive half slots. We show the case of successful decoding at the partner. Decoding As described in Section 3.3.1, there are four possible cases depending on whether each source decodes correctly or not its partner information. Without loss of generality, we considerdecodingofu 1 atthedestinationassumingthatsources 2 correctlydecodedthe information of source s 1. The destination receives a noisy version of c 1 (t) transmitted by source s 1 and a noisy version of u 2 (t)g L π(u 1 (t 1))G R transmitted by source s 2. Iterative decoding is used at the destination to exchange extrinsic information about u 1 between the corresponding SISO decoders. Simulation Results Figure 3.20 shows simulation results of the system proposed in [XFKC07]. Each packet consists of k = 500 bits. All channels are subject to block Rayleigh fading. The fad-

91 60 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS 10 0 no coop algebraic code superposition 10-1 FER γ b sd Figure 3.20 FER curves over Rayleigh block fading channel; k = 500 bits; R eff = 1/3; 10 iterations. ing is constant over the time slot. For the non-cooperative transmission, the rate-1/3 convolutional code with generator polynomials (15,13,17) 8 is used. For the cooperative scheme, the rate-1/3 recursive convolutional code with generator polynomials (1, 13, 17) is used by each source to encode its own information and the rate-1/3 recursive convolutional code with generator polynomials ( 02, 13, 17) is used by the source to encode its partner information. The two partner nodes employ an 8-state BCJR decoder while a 64-state BCJR decoder is required at the destination. As shown via simulations, the proposed approach presents both coding and diversity gain with respect to the non-cooperation transmission. Moreover, transmitting the algebraic superposition of the locally generated codeword and the relayed codeword makes efficient use of available resources. This design was referred to as network coding because it features the algebraic superposition of the channel codes over a finite field which fits the definition of network coding. We presented above an orthogonal scenario where orthogonality is obtained by time sharing. Non-orthogonal scenarios are known to achieve higher spectral efficiency. Thus, we are interested in studying a non-orthogonal scenario where sources s 1 and s 2 transmit in the same time slot. The destination receives therefore a superposition of the signals transmitted by both sources and a multiuser detection technique is required at the destination. In the following section, we describe the considered scenario.

92 3.3. CODED COOPERATION IN A TWO-USER SCENARIO 61 Table 3.3 Transmission time for two time slots t 1 t 2 d c s 1 + cs 2 w 1 s + ws 2 s 2 Tx Tx s 1 Tx Tx Network Coding in Non-Orthogonal Two-User Cooperative Scenario We consider the same network as depicted in Figure The two sources s 1 and s 2 are allowed to transmit simultaneously. This involves that both sources must be full-duplex. In this scenario, the destination receives a superposition of the signals transmitted by the sources. Several transmitting approaches can be used to deal with multiple-access interference at the destination, such as code-division multiple-access (CDMA) [LV89] and interleave-division multiple-access (IDMA) [PLWL03a]. Here, we consider the use of IDMA for multiuser detection at the destination. TheprincipleofIDMAtechniqueisexplainedinChapter2,andthestructuresofthe IDMA transmitter and the IDMA receiver are presented in Sections and , respectively. As in Section 3.3.2, sources s 1 and s 2 encode the information sequences u 1 and u 2 into codewords c 1 and c 2, respectively. The sequences c 1 and c 2 are then spread by using a repetition code into sequences c s 1 and c s 2, respectively. We denote by m the spreading factor. Finally, sequences c s 1 and c s 2 are scrambled by interleaver π 1 and π 2 into the so-called chip sequences c s 1 and c s 2, respectively. As described in Section 3.3.2, each source attempts to decode its partner information and if decoding succeeds, each source computes the algebraic superposition w i, i = 1,2 of its own codeword c i and codeword c i, i = 1,2. The resulting codewords will be spread by the spreading code of factor m into codewords w s i, i = 1,2 which will be in their turn interleaved by interleaver π i, i = 1,2 into codewords w s i, i = 1,2. In Table 3.3, we illustrate the transmission time for two time slots when decoding of the partner information is successful at each source. Figure 3.21 shows BER curve of the simulated system. The rate-1/2 recursive convolutional code with generator polynomials (05,07) 8 is used by each source to encode its own information and the rate-1/2 recursive convolutional code with generator polynomials (03,07) 8 is used by the source to encode its partner s information. A repetition code of factor m = 4 is used for spreading. For comparison, we consider the scenario where two users transmit simultaneously and IDMA technique is used for multiuser detection. A frame of length k = 4096 bits is considered and fifteen iterations are performed. As shown in Figure 3.21, the cooperative scheme outperforms the non cooperative one. For instance, at BER 10 3, 2 db are gained by cooperation. We also compare the performance of the non-orthogonal scenario with the orthogonal one. In Figure 3.22, we plot the BER curves of both non-orthogonal and orthog-

93 62 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS No Coop m=4 Algebraic code superposition, m= BER γ b sd [db] Figure 3.21 BER curve over AWGN channel; k = 4096 bits, 15 iterations Orthogonal Scenario IDMA, coop, m= BER γ b sd [db] Figure 3.22 BER curve over AWGN channel; k = 500 bits, 10 iterations. onal scenario described in Section The curve corresponding to the orthogonal scenario represents the genie-aided curve for the non-orthogonal scenario. A frame of length k = 500 bits is considered and ten iterations are performed. A spreading factor m = 2 is required to approach the genie-aided curve, with a loss around db. Since a spreading factor m 2 is required to achieve the orthogonal performance, the

94 3.3. CODED COOPERATION IN A TWO-USER SCENARIO 63 system with IDMA does not achieve spectral efficiency gain. With m = 2, the spectral efficiency remains the same for both scenarios. We conclude that time sharing between the two sources is the best choice for this scenario. The advantage of non-orthogonal scenarios in terms of improved spectral efficiency will be observed for a large number of users q (when m q). However, extending the network coding approach of [XFKC07] to a large number of user is not straightforward since the complexity at the decoders becomes very high. In the next chapter, we consider a general network with large number of users and we propose a distributed turbo-like code for such a network.

95 64 CHAPTER 3. COOPERATIVE COMMUNICATIONS IN WIRELESS NETWORKS 3.4 Conclusions In this chapter, we presented the concept of cooperative communications and we considered three cooperative networks: the relay channel, the MARC, and the two-user cooperative network. For the relay channel, we first described the three main protocols of cooperation at the relay: amplify-and-forward (AF), decode-and-forward (DF) and compress-and-forward (CF). We restricted ourselves to scenarios where DF outperforms other protocols. We further gave theoretic limits in terms of achievable rates and outage probability and showed how cooperation can achieve higher rates and diversity order. We also gave an overview of some coding schemes for the relay channel in particular the DPCCs and the DSCCs. For the two-user MARC, achievable rates were computed and maximized by optimally allocating the transmission time between the two sources and the relay and an outage analysis was given which is relevant when channels exhibit Rayleigh block fading. We further described two encoding strategies for the two-user MARC which jointly exploit channel and network coding ([HD06] and [YK07]) and outperform the non-cooperative system. We focused on the strategy proposed in [YK07] where the relay, after decoding the received messages from both sources, uses the soft decisions on the codewords of both sources to compute the LLRs of the codewords combination. We established a comparison with the case when the relay decodes and adds the hard decisions of the two codewords and we showed that the approach in [YK07] is beneficial only when the SNR of the source-to-relay channel is very poor. This is equivalent to a scenario where the relay is far from the sources. The third part of this chapter was devoted to describe the two-user cooperative scenario. In this scenario, each source acts as a relay for its partner. We presented the coded cooperation for this scenario and we summarized an approach proposed in [XFKC07] which investigates network coding and achieves diversity and coding gain with respect to direct transmission. We also studied the network coding approach in a non-orthogonal scenario where IDMA is used to separate the different signals. We showed that, for this scenario, considering TDMA is a better choice than simultaneous multiple-access because the spreading factor required is equal to the number of users (m = 2) and no spectral efficiency gain is achieved. Until now, we have considered networks with at most two sources. In the next chapter, we consider a more general relay network, where multiple sources transmit to a destination with the help of a relay and we propose a distributed coding scheme for such a network.

96 CHAPTER 4 Distributed Turbo-Like Codes for Multiuser Cooperative Scenarios In the previous chapter, we reviewed some distributed coding schemes for networks with relays, in particular for the relay channel and the MARC with two sources. In this chapter, a more general scenario is considered. We consider a network where multiple sources communicate with a destination with the help of a relay. A typical scenario for the proposed coding scheme is a wireless sensor network where several sensors process small amounts of information and communicate to a destination with the help of a central node, which has less stringent restrictions on resources than the sources. We propose a distributed turbo-like coding scheme for a multi-source relay scenario where multiple sources transmit to a destination aided by a common relay, which uses the decode-and-forward strategy and operates in half-duplex mode. In this chapter, we consider an orthogonal scenario obtained by means of TDMA. The relay decodes the information from the sources and it properly combines and re-encodes them to generate some extra redundancy, which is forwarded to the destination. The amount of redundancy generated by the relay can simply be adjusted according to requirements in terms of performance, throughput and/or power. Decoding at the destination of the information of all sources is performed jointly exploiting the redundancy provided by the relay in an iterative fashion. The overall communication network can be viewed as an SCC, where the outer encoder groups the encoders of the sources and the inner encoder is the relay. Accordingly, the receiver can decode users data using a decoding strategy that resembles the decoding of an SCC. The remainder of this chapter is organized as follows. The system model is described 65

97 66 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS r d Figure 4.1 A wireless relay network: multiple sources transmit to a single destination with the help of a common relay. in Section 4.1. In Section 4.2, we introduce two different encoding strategies at the relay, named Strategies A and B. We further present the overall network as an SCC in Section 4.3 and we describe the decoding process at the receiver. Section 4.4 addresses the optimization of the overall code. Section 4.5 discusses some information theoretic limits in terms of achievable rates, transmission time allocation and outage rates. Convergence properties of the proposed distributed SCC are addressed in Section 4.6 by means of an EXIT chart analysis and simulation results are given in Section 4.7. In Section 4.8, we present a way to improve the decoding process when the transmission to the relay is not reliable. Finally, conclusions are drawn in Section 4.9. The results of this chapter were published in [YG10] and [YG11]. 4.1 System Description System Model In this section, we describe the scenario under consideration and the channel model. We consider the wireless relay network depicted in Figure 4.1. The network consists of q sources, s 1,...,s q, which communicate statistically independent data to a single destination d cooperating through a common relay r. The relay uses the decode-and-forward strategy and operates in half-duplex mode according to a time-division transmission schedule. In this chapter, we consider orthogonal scenarios. Orthogonality is obtained via TDMA. The transmission time is then divided into q + 1 time slots. At source s i, i = 1,...,q, the k i -bit information sequence u si is encoded by encoder C i of rate R i into codeword c si of length n i = k i /R i bits. Codeword c si is modulated into x si which is transmitted over the wireless channel at time slot i. Here, we consider BPSK modulation. Due to the broadcast nature of the wireless channel, the relay receives a noisy observationofthemodulatedcodewordsx si,denotedbyy si r,fromthedifferentsources.

98 4.1. SYSTEM DESCRIPTION 67 After decoding the received signals, the relay generates an additional parity c r. It then cooperates with the sources by transmitting the modulated version x r of its own parity sequence c r to the destination at time slot q + 1. In Section 4.2, we describe how the relay encodes and generates c r. The destination decodes the information of the q sources by jointly exploiting the received sequences y si d from the sources and the sequence y rd from the relay Channel Model The channel model is a generalization of the the two-user MARC presented in Chapter 3. As shown in Figure 4.1, there are three directed transmission links under consideration: the links from the sources to the destination, l si d, the links from the sources to the relay, l si r, and the link from the relay to the destination, l rd. We denote by γ si d, γ si r and γ rd the SNR of the i-th source-to-destination channel, the i-th source-to-relay channel, and the relay-to-destination channel, respectively. Likewise, we denote by d si d, d si r and d rd the distance from source s i to the destination, from source s i to the relay, and from the relay to the destination, respectively. In our work, we make several assumptions: A1: For simplicity, all sources are at the same distance from the destination, i.e., d si d = d sd i. Therefore, γ si d = γ sd for all sources s i. A2: All sources are at the same distance from the relay, i.e., d si r = d sr for all sources s i. Therefore, γ si r = γ sr i. A3: The relay is closer to the sources than to the destination unless otherwise stated. This is a favorable and necessary assumption for decode-and-forward techniques, since it guarantees a low error probability at the relay. A4: As in Sections 3.1 and 3.2, the SNR of the three channels under consideration are linked by γ sr = g sr γ sd, γ rd = g rd γ sd, (4.1) where the gains g sr and g rd are due to shorter transmission distances and are given by g sr = (d sd /d sr ) α and g rd = (d sd /d rd ) α, respectively. α denotes the pathloss exponent and it is often assumed to be 2 α 6 [Yac93, Rap99]. The received observations at the the relay and at the destination can be written as y si r = 2γ sr H si rx si +z si r, y si d = 2γ sd H si dx si +z si d, y rd = 2γ rd H rd x r +z rd, (4.2)

99 68 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS where z si r, z si d and z rd are AWGN noise vectors with zero-mean, unit-variance i.i.d. elements, and H si r, H si d and H rd are diagonal matrices with Rayleigh fading channel coefficients in the main diagonal and zeros everywhere else. 4.2 Encoding Strategies at the Relay In this section, we describe two novel encoding strategies at the relay for the multisource relay network. The proposed relaying scheme can be regarded to as a decode-andforward scheme. The relay receives a noisy observation of the codewords c si from the q sources, it decodes them, and generates an estimate of the transmitted codewords. The estimatedcodewordsĉ i arethenproperlycombined,interleavedinto cbyaninterleaver Π,andre-encodedbyanotherencoderC e priortotransmission.twoencodingstrategies at the relay are devised in this section, called Strategy A and Strategy B Encoding Strategy A The bits of codeword c at the output of the interleaver, of length N = q i=1 n i bits, are grouped into groups of J bits and passed to an SPC circuit. This simply forms the sum modulo-2 of the J incoming bits, i.e., for each group of J bits it generates a single bit as their modulo-2 sum. The codeword at the output of the SPC, of length N SPC = N/J bits, is then encoded by a recursive convolutional encoder C e (typically of rate R e = 1) and is transmitted over the wireless channel. The effective code rate of the overall system is R eff = K/N, where K = q i=1 k i and N = N +n r, n r = N SPC /R e = N/R I being the length of the codeword transmitted by the relay, where R I = JR e. The proposed distributed coding scheme is depicted in Figure 4.2. Parameter J determines the amount of redundancy transmitted by the relay, i.e., given R i and q it determines the effective code rate of the overall system. J can be adjusted according to the requirements in terms of performance, overall system rate and/or power constraints Encoding Strategy B The bits of the codeword c are encoded by a recursive inner encoder C e (typically of rate R e = 1) heavily punctured to rate R I = R e /ρ p > 1 through a puncturer P and transmitted to the destination. A puncturer P is defined by a puncturing pattern p of puncturing period N p. Let δ p (0 δ p N p ) denote the number of bits remaining at the output of the puncturer within a puncturing period N p. We denote by ρ p = δ p /N p (0 ρ p 1) the permeability ratio of the puncturer, giving the ratio of bits that survive puncturing. Note that ρ p = 0 corresponds to the non-cooperation case. The effective code rate of the overall system is R eff = K/N, where N = N + n r and n r = N/R I. Note that while the encoder at the relay is of rate higher than one

100 4.3. THE RELAY NETWORK REGARDED AS A SERIALLY CONCATENATED CODE 69 AWGN AWGN relay operation AWGN AWGN M U X Π S P C AWGN AWGN AWGN Figure 4.2 Block diagram of the proposed coding scheme. The relay processes information using strategy A. (and therefore non-invertible), the overall distributed coding scheme is of rate R eff < 1, which allows correct recovering of users data. The block diagram of this distributed coding scheme is depicted in Figure 4.3. The permeability ratio ρ p determines the amount of redundancy transmitted by the relay and can be adjusted according to performance and power constraints requirements. Notice that strategy B allows for a finer control of the redundancy transmitted by the relay than strategy A, if N p is large enough, and therefore yields a higher flexibility. 4.3 The Relay Network Regarded as a Serially Concatenated Code TheproposeddistributedcodingschemecanbeseenasanSCCwheretheouterencoder accounts for the encoders C i of the q sources, and the inner encoder is the relay. The equivalent representation is depicted in Figure 4.4. The information sequences u si are concatenated and encoded by the outer encoder C O. If encoders C i are different, C O is time-variant. The encoded information is transmitted over a wireless channel with SNR γ sd, corresponding to the direct link between the sources and the destination, l sd. It is also interleaved and re-encoded by the inner encoder C I, of rate R I, which implements strategy A or B. The resulting codeword is transmitted over a wireless channel with SNR γ rd. Note that unlike in a classical SCC scheme, the codeword at the input of the

101 70 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS AWGN AWGN relay operation AWGN AWGN M U X Π punct. AWGN AWGN AWGN Figure 4.3 Block diagram of the proposed coding scheme. The relay processes information using strategy B. Π S P C punct. Figure 4.4 Equivalent representation of the wireless relay network of Figure 4.2 and Figure 4.3. inner encoder may contain errors. From the equivalent representation in Figure 4.4, the SCC resulting from strategy A is similar to the coding scheme introduced in [CTD + 05], nicknamed FlexiCode. For more details on the FlexiCode, we refer the reader to Sections and In [CTD + 05] an SPC circuit is used before the inner encoder of an SCC to increase the code rate while preserving very good performance in the error floor. Moreover, a copy of the input data is sent directly to the channel, i.e., the code is systematic. Here, the key idea is to use an SPC to group several users and to control the rate of the relayto-destination link, instead of increasing the code rate. The overall scheme is therefore

102 4.3. THE RELAY NETWORK REGARDED AS A SERIALLY CONCATENATED CODE 71 (1) (5) (2) P/S Π SPC decoder Π -1 S/P (4) (3) (1) (5) Figure 4.5 Joint iterative decoding when the relay operates using strategy A. We enumerate the decoding steps (scheduling) from (1) to (5). a form of non-systematic distributed FlexiCode. On the other hand, the SCC resulting from strategy B is similar to the SCC scheme proposed in [GMV05, GMV09] (see Sections and 2.4.3). In [GMV05, GMV09] an SCC was proposed where the inner encoder was heavily punctured beyond the unitary rate. This feature allows keeping a very low error floor for a wide range of code rates since the interleaver gain is preserved, and achieves much better performance than standard SCCs, especially for high rates. Here, the level of puncturing of the inner code is used to group several users instead of increasing the code rate. The coding schemes in [CTD + 05] and [GMV05, GMV09] are the best known SCCs for high coding rates. They also allow a high flexibility in terms of code rate. In terms of the wireless network of Figure 4.1 high rates in a classical SCC correspond to a high number of users. Therefore, the proposed schemes are expected to perform very well even for a large number of users Decoding of the Distributed Serially Concatenated Code According to the equivalent representation in Figure 4.4, decoding of users data can be performed using a decoding strategy that resembles the decoding of an SCC: decoding of the information of all sources can be done jointly, exploiting the redundancy provided by the relay in an iterative fashion Decoding for Strategy A For the FlexiCode presented in [CTD + 05], the systematic nature of the code means that the decoding must commence with the outer code. However, in our scheme other schedulings can be used since codewords for both outer and inner codes are sent through the channels. Figure 4.5 illustrates the iterative decoding at the destination when the relay encodes using strategy A. One possible, but not unique, scheduling for strategy

103 72 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS (1) (3) P/S Π Depunct. (2) Π -1 S/P (1) (3) Figure 4.6 Joint iterative decoding when the relay operates using strategy B. We enumerate the decoding steps (scheduling) from (1) to (3). A is as follows: The relay-to-destination channel metrics L ch (c r ) are fed to the inner decoder C 1 I, and the source-to-destination channel metrics L ch (c si ), i = 1...,q, are fed to each source decoder C 1 i. The receiver decodes first the sources and generates extrinsic information L e (ĉ) on codeword ĉ. (1) 1 The SPC code is decoded in the outer-inner direction by using this extrinsic information as a priori information after been properly interleaved. The SPC decoder generates extrinsic information at its input and at its output. (2) The convolutional code of the relay is decoded using channel information L ch (c r ) and a priori information on its input provided by the SPC decoder. (3) The SPC code is decoded in the inner-outer direction using the a priori information generated by the decoder of the outer code and the decoder of the inner code. (4) Finally, the sources are decoded again using channel information L ch (c si ), and a priori information generated by the SPC decoder, L a (c si ), after been properly de-interleaved. This completes a single iteration. (5) The process is repeated until the maximum number of iterations is reached or an early stopping criterion is fulfilled Decoding for Strategy B Figure 4.6 depicts the iterative decoding at the destination when the relay encodes using strategy B. One possible scheduling of the iterative decoding for strategy B is as follows: 1 The number between brackets corresponds to the decoding steps in Figure 4.5.

104 4.4. CODE OPTIMIZATION 73 The relay-to-destination channel metrics L ch (c r ) are passed after de-puncturing to the inner decoder, and the source-to-destination channel metrics L ch (c si ) are passed to each source decoder. The receiver decodes first the sources and generates extrinsic information L e (ĉ) on codeword ĉ. (1) 2 The convolutional code of the relay is decoded using channel information L ch (c r ) anda priori informationonitsinput,l a ( c),providedbythedecoderofthesources after proper interleaving. (2) The sources are decoded using channel information L ch (c si ) and a priori information generated by the inner decoder, L a (c si ), after proper de-interleaving. This completes a single iteration. (3) This process repeats for a certain maximum number of iterations or until it satisfies an early stopping criterion A Particular Case: The Overall Network Performing as a Parallel Concatenated Code In Figures 4.2 and 4.3, instead of generating an estimate of codewords c si the relay may estimate information words u si. The estimates û si are then properly combined, interleaved and encoded by encoder C e using strategy A or B as described before. The resulting relay network effectively realizes a (asymmetric) distributed PCC; the upper encoder of the PCC accounts for encoders C i of the q sources and the lower encoder corresponds to the relay. Decoding of the resulting code is performed using a classic decoding of PCC. The scheduling for strategies A and B is similar to the one described in Section 4.3.1, the main difference being that the extrinsic exchange between decoders is on the information bits u i. The expected behavior is that the overall system performing as a PCC presents a better convergence behavior, while better error floor performance is obtained when performing as an SCC. 4.4 Code Optimization The performance of the proposed distributed codes depends on encoders C i and C e and on J and (p,δ p ) for strategy A and strategy B, respectively. Given q and the overall system rate R eff, the goal is to optimize these parameters to ensure good performance in both the error floor and waterfall regions. For simplicity and flexibility, we consider very simple rate-1/2, 4-state convolutional encoders for C i, which can be punctured 2 The number between brackets corresponds to the decoding steps in Figure 4.6.

105 74 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS to the desired rate R i. Stronger codes, such as turbo codes, can also be used, at the expense of a more complex decoder at the destination. Furthermore, for the scenario considered here (the relay is closer to the sources than to the destination) the use of stand-alone codes at the sources leads to better convergence compared to iteratively decodable codes, while good error floors are yet achieved. A joint optimization of the encoders polynomials and of J and (p,δ p ) to optimize the error floor and the convergence threshold is prohibitively complex. Therefore, we consider the following strategy, yet feasible: first, the encoder polynomials of C i and C e (and the puncturing pattern p for strategy B) are chosen according to design criteria for the error floor [BDMP98]. Then, time allocation, i.e., parameters J and ρ p and the rates R i are optimized according to other criteria. In this work, we optimize the time allocation according to two criteria: in Section we analytically optimize the time allocation to maximize the achievable rates; in Section 4.6 we use EXIT charts to minimize the decoding thresholds. We consider the same encoder for all sources. For strategy A, the same optimal (in terms of error floor for a fixed complexity) 4-state, rate-1/2, feedforward convolutional encoder with generator polynomials (5,7) 8 in octal notation is used at each source, and the 4-state, rate-1, recursive convolutional encoder with generator polynomial (3/7) 8 is used for C e [CTD + 05]. For strategy B, the same optimal 4-state, rate-1/2, recursive convolutional encoder with generator polynomials (1,5/7) 8 is used at each source [GMV05, GMV09]. According to [BDMP98] it can be convenient to choose as outer code a nonrecursive encoder. Here, for simplicity, we considered identical encoders for C i and C e. Moreover, it is worth mentioning that the difference in performance is marginal. The optimal 4-state, rate-1, recursive convolutional encoder with generator polynomial (5/7) 8 is used at the relay [GMV05, GMV09]. Also, the puncturing pattern p in [GMV05, GMV09], which is optimized for the error floor, is used. Notice that for both strategies, encoder C e must be recursive to provide an interleaver gain. Notice also that for strategy A we do not use the optimal encoder for C e, but instead we use the encoder (3/7) 8 proposed in [CTD + 05]. This is because the optimal encoder entails some loss in terms of convergence. 4.5 Information Theoretic Limits In this section, we present an information theoretic analysis of the proposed system. We give the achievable rates over the time division MARC with q sources. We first consider equal time allocation between the q sources and the relay and later we compute the optimal time allocation to maximize the achievable rates. We further analyze the outage behavior of the proposed system over Rayleigh block fading channels.

106 4.5. INFORMATION THEORETIC LIMITS 75 Table 4.1 Minimum γsd b that achieves a rate of R eff = q 2(q+1) when equal time is allocated for the sources and the relay γ b min,eq, dsr = (1/4)d sd γ b min,eq, dsr = (1/2)d sd R eff q = db db q = db db 0.4 q = db db q = db db q = db db q = db db 0.49 q = db db Achievable Rates In this section we compute the achievable rates for the multi-source relay network of Figure 4.1. In Section 3.2.1, we considered the time division MARC with two sources and one relay and we gave the achievable decode-and-forward rates following the approach in [Hau08]. A similar analysis can be performed for the multi-source scenario withq sourcesbygeneralizing(3.22)and(3.24)ofchapter3.inthissection,wegivethe results for the generalized multiuser case for both equal and optimal time allocation Achievable Rates with Equal Time Allocation We first consider equal time allocation for sources s i, i = 1,...,q, and the relay (θ i = θ r = 1/(q+1)), which corresponds to the case where the relay and the sources transmit the same amount of information. Also, we assume γ si d = γ sd i and γ si r = γ sr i (Assumptions A2 and A3 of Section 4.1.2). Under the assumption that all sources transmit at the same rate (R i = R s i), the achievable rate is given by R i = R s = min { 1 q +1 C(γ sr), 1 q +1 C(γ sd)+ } 1 q(q +1) C(γ rd). (4.3) The rate of the overall system, also referred to as the sum rate, is R eff = qr i. Let γsd b = γ sd/r eff denote the SNR (in db) per information bit. In Table 4.1 we report the minimum value of γsd b, denoted by γb min,eq, such that a system rate R eff = q is achieved for a Rayleigh fast fading channel and several values of q. We have 2(q+1) consideredthateachsourcetransmitswithacoderater i = R = 1/2.Sinceweconsider equal time allocation, the source and the relay transmit the same amount of symbols, therefore n s = n r = k/r = 2k. Thus, the effective rate of the overall system depending on the number of users q is given by R eff = qk q2k +2k = q 2(q +1) (4.4)

107 76 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS In the computation, we assumed BPSK modulation. In Table 4.1, we give γ b min,eq for two positions ofthe relay: we first consider that therelay is at halfdistance between the sources and the destination, d sr = (1/2)d sd and d rd = (1/2)d sd, and we also consider that the relay is closer to the sources than to the destination, i.e., d sr = (1/4)d sd and d rd = (3/4)d sd. From Table 4.1, we observe that higher rates can be achieved when the relay is at half distance between the sources and the destination. For instance, for q = 2 a rate R eff = can be achieved for γ b min,eq = db when the relay is at half distance between the sources and the destination while γ b min,eq = db when d sr = (1/4)d sd. A gain of almost 2.7 db can be achieved when the relay is positioned in the middle. This follows directly from (4.3) Achievable Rates with Optimal Time Allocation Depending on the channel conditions, the time allocation can be smartly allocated between the sources and the relay as done in Section The transmission time parameters can be optimized to maximize the achievable rates. In Section , we computed the achievable rates and the optimal time parameters for the two-user MARC. The optimal time allocation and the achievable rates for the symmetric MARC with q sources can be derived in a similar way. The optimal time allocation θ i for source s i and relay r is given by and θ opt i = 1 q C(γ rd ) C(γ rd )+C(γ sr ) C(γ sd ) = θopt s i (4.5) θ opt r = 1 q i=1 θ opt i while the achievable rate for source s i is given by = 1 qθ opt s, (4.6) R i = 1 q C(γ sr )C(γ rd ) C(γ rd )+C(γ sr ) C(γ sd ) i. (4.7) The sum rate R eff = qr i of the overall system is given by R eff = C(γ sr )C(γ rd ) C(γ rd )+C(γ sr ) C(γ sd ). (4.8) From (4.8), we observe that the MARC achieves the same sum capacity of the relay channel and therefore the optimization problem can be treated as a capacity optimization problem for a single user relay channel [Hau08]. In Table 4.2 we report the optimal time allocation parameters θs opt, θr opt and the minimum value of γsd b, denoted by γb min,opt, such that a system rate R eff = q is 2(q+1) achieved over a fast fading channel and several values of q. In the computation, we first assumed d sr = (1/4)d sd and d rd = (3/4)d sd. An improvement of 1.4 to 2.2 db with respect to equal time allocation is observed, depending on the number of sources. We

108 4.5. INFORMATION THEORETIC LIMITS 77 Table 4.2 Minimum γsd b that achieves a rate of R eff = q 2(q+1) and optimal time allocation parameters for the distributed serially concatenated schemes for different number of users d sr = (1/4)d sd and d rd = (3/4)d sd d sr = (1/2)d sd and d rd = (1/2)d sd γmin,opt b θs opt θr opt γmin,opt b θs opt θr opt q = db db q = db db q = db db q = db db q = db db q = db db q = db db R eff d γ sd [db] 5 10 Figure 4.7 Achievable sum rate as a function of γ sd and the relay position: At low SNRs the peak is reached for d=0.5. also report θs opt, θr opt and γmin,opt b for d sr = (1/2)d sd and d rd = (1/2)d sd. As in the case of equal time allocation, higher rates are achieved when the relay is positioned at half distance from the sources and the destination. In Figure 4.7, we plot the achievable sum rate as a function of γ sd and the parameter d = d sr /d sd. It can be observed that the achievable sum rate reaches its peak value for d = 0.5. For optimal time allocation the rate R I of the relay encoder of the proposed distributed SCCs is given by R I = 1/(1 qθ opt s ) 1. Also, for a given overall system rate

109 78 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS R eff = q the rate of each encoder C 1 2(q+1) i must satisfy R i =. Varying R 2θs opt (q+1) I is very simple by tuning parameters J and ρ p in strategy A and strategy B, respectively (see Section 4.2), while different code rates R i can be obtained by puncturing a mother encoder C i. Therefore, the proposed scheme offers a high flexibility. Notice that strategy B allows for a finer approximation of R I, since ρ p provides a high resolution if N p is large enough. From the values of θs opt in Table 4.2, we obtain that for d sr /d sd = 1/4 the optimal rate R i for the sources is around 0.98 for all values of q. Unfortunately, it is hard to design good codes for such a high rate. In particular, a heavy puncturing of a convolutional code leads to a poor code and thereby to poor performance. In order to optimize the time allocation in such case, i.e., when analytical results give unfeasible code parameters (R i ), we use EXIT charts. This optimization by means of EXIT charts is presented in Section Outage Behavior over the q-marc In this section, we study the outage behavior of the proposed system over Rayleigh block fading channel. An outage event is declared if the data of at least one source is not decoded reliably at the destination. We denote by e out the outage event, and by ē out its complement. In Section 3.2.2, we computed the outage rate for the MARC with two sources. The analysis for multiple sources (q > 2) is similar and requires considering all possible cuts. The resulting event ē out is similar to the case q = 2 in (3.37) with more conditions. ē out is given by {[ ( ē out = k i )] [ ( )]} n i C(γ si r) k j n j C(γ sj d)+n r C(γ rd ) G S i G i G G S j G j G { } (k l n l C(γ sl d)) l S (4.9) for all G and G subsets of S where S = {1,...,q}. For S = {1,2}, we get ē out in (3.37). In Figure 4.8, we show the outage probability over the MARC with q = 4,8 and 20. For comparison purposes, we consider the outage event over a multiple-access channel (MAC) with q sources. An outage is declared when the information of at least one of the q sources is not decoded successfully. The outage event is then given by ē out = ( q i=1 q i ) e out i s ē q i out s. (4.10) Figure 4.8 shows the gain that can be achieved by cooperation with respect to noncooperation. For instance, for an outage probability equal to 10 2, a gain of 15 db can

110 4.6. EXIT CHART ANALYSIS q=4 q=8 q=20 Outage probability γsd [db] Figure 4.8 Outage probability over the MARC for q = 4,8 and 20 for an overall rater eff = q 2(q+1) (solidcurves)andoutageprobabilityforthenoncooperativesystem (dashed curves). be achieved through cooperation for a number of users q = 20. Note that this outage probability is a lower bound on the FER of the proposed system. We conclude that the MARC offers advantageous outage behavior and diversity order with respect to the direct transmission. The diversity gain is observed by the change in the slope of the outage probability curves. These results serve as the benchmark for the FER of the proposed system. 4.6 EXIT Chart Analysis As explained in Section 2.5, EXIT charts are analytical tools to analyze the convergence behavior of iterative decoding. The equivalent representation of the wireless relay network in Figure 4.4 allows applying standard tools for the analysis of SCCs to analyze the performance of the proposed distributed coding scheme. In this section, we compute the convergence thresholds of the proposed distributed SCCs through an EXIT chart analysis [tb01a]. For convenience, the equivalent representation of the multi-source wireless network in Figure 4.4 is further redrawn in the form of Figure 4.9, where the outer encoder is not directly connected to the channel. Then, the contribution of the direct link

111 80 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS Figure 4.9 Another equivalent representation of the distributed SCC of Figures 4.2 and 4.3. between the sources and the destination is moved to the inner encoder C I through its systematic branch. Note that the link l sd corresponds to the concatenation of l sr and l sd in Figure 4.9. Also, note that for analysis purposes, representations in Figures 4.4 and 4.9 are equivalent. We assume that γ sr is high enough, so that no error occurs at the relay. In this case, the convergence behavior of the distributed turbo-like code in Figures 4.2 and 4.3 can be tracked using standard EXIT charts by plotting in a single chart the EXIT curve of the outer encoder C O (which is now independent of γ sd ) and the EXIT curve of the inner encoder C I, which depends on both γ sd and γ rd EXIT Charts with Equal Time Allocation We first consider equal time allocation between the q sources and the relay, i.e., the q sources and the relay transmit the same amount of symbols. For strategy A and strategy B, we use the encoding parameters of C O and C e according to the cde optimization explained in Section 4.4. For strategy A, equal time allocation is equivalent to set J = q, i.e., R eff = q. For strategy B, equal time 2(q+1) allocation translates into setting ρ p = 1/q, i.e., only one bit out of q at the output of encoder C e is preserved. Note that with this choice of ρ p the rate of the link l rd is kept constant independently of the number of users, and R eff = q. Finally, we first 2(q+1) assume that d sr = (1/4)d sd and d rd = (3/4)d sd, which translate into g sr = db and g rd = 4.39 db, respectively (see Section 4.1). In Figures 4.10 and 4.11, we plot the transfer functions of the outer decoder C 1 O and the equivalent inner decoder C I 1. As shown in Figure 4.10, a tunnel between the EXIT curve of the outer encoder and the EXIT curve of the inner encoder opens at γsd b = 0.77 db and γb sd = 1.57 db for q = 2 and q = 4 users, respectively, indicating convergence around these values. In Figure 4.11, the tunnel is observed at γsd b = 2.32 db and γsd b = 3.52 db for q = 8 and q = 20 users, respectively. The estimated convergence thresholds are given in Table 4.3 for q = 2,4,8,20,30,50 and 100 users and strategies A and B. The estimated convergence thresholds are similar for both strategies. We observed that the predicted thresholds match with simulation

112 4.6. EXIT CHART ANALYSIS ,9 0,8 C O C' I, q=2 (0.77dB) C' I, q=4 (1.57dB) 0,7 Ie(C'I), Ia(CO) 0,6 0,5 0,4 0,3 0,2 0, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 I a(c' I), I e(c O) Figure 4.10 EXIT chart of the proposed distributed turbo-like code, strategy B, for q = 2 and q = 4 users. Fast fading Rayleigh channel. d sr = (1/4)d sd and d rd = (3/4)d sd. R eff = q 2(q+1). The convergence threshold for q = 2 is γb sd = 0.77 db and for q = 4 is γsd b = 1.57 db. Table 4.3 Convergence thresholds for the distributed serially concatenated schemes for different number of users d sr /d sd = 1/4 Threshold (A) Threshold (B) q = db 0.77 db q = db 1.57 db q = db 2.42 db q = db 3.52 db q = db 4.00 db q = db 4.66 db q = db 5.40 db results for very long block sizes even if some errors occur at the relay (i.e., when γ sr is limited). The proposed distributed SCCs perform within 1.5 to 2.0 db from capacity for a number of users up to q = 20 (see Table 4.3). For higher q the gap to capacity increases. We also consider the case when the relay is at half distance between the sources and the destination (d sr = (1/2)d sd and d rd = (1/2)d sd ). In Table 4.4, we report the estimated convergence thresholds for q = 2,4,8,20,30,50 and 100 users and strategies A and B. An improvement of 0.2 to 2.6 db in the convergence threshold is observed with respect to the case when d sr /d sd = 1/4.

113 82 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS 1 0,9 0,8 C O C' I, q=8 (2.32 db) C' I, q=20 (3.52 db) 0,7 Ie(C'I), Ia(CO) 0,6 0,5 0,4 0,3 0,2 0, ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 I a (C' I ), I e (C O ) Figure 4.11 EXIT chart of the proposed distributed turbo-like code, strategy A, for q = 8 and q = 20 users. Fast fading Rayleigh channel. d sr = (1/4)d sd and d rd = (3/4)d sd. R eff = q 2(q+1). The convergence threshold for q = 8 is γb sd = 2.32 db and for q = 20 is γsd b = 3.52 db. Table 4.4 Convergence thresholds for the distributed serially concatenated schemes for different number of users for d sr /d sd = 1/2 Threshold (A) Threshold (B) q = db -1 db q = db 0.65 db q = db 1.9 db q = db 3.35 db q = db 3.8 db q = db 4.2dB q = db 5.3 db EXIT Charts with Optimal Time Allocation EXIT charts can be used to optimize the time allocation so that the convergence threshold of the distributed SCCs is minimized. In particular, we consider strategy B, which allows for a finer approximation of the optimal time allocation. We assume that all sources transmit at the same rate R i = R s and we find the pair (R s,ρ p ), equivalently (R s,r I ), which minimizes the convergence threshold. To simplify the search, we limit R s to the set {0.5,0.55,...,0.95}. The rate R s is obtained by randomly puncturing the rate-1/2 convolutional encoder. We denote by R s the value of R s which minimizes

114 4.6. EXIT CHART ANALYSIS 83 Table 4.5 Convergence thresholds for the distributed serially concatenated schemes for different number of users with optimal time allocation Threshold (B) Threshold (B) θ s θ r R s q = db db q = db db q = db 0.3 db q = db 0.75 db q = db 0.9 db q = db 1.0 db q = db 1.05 db ,9 0,8 Ie(C'I),Ia(CO) 0,7 0,6 0,5 0,4 0,3 0,2 0,1 C O C' I, q=4 (-0.35 db) 0 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 I a (C' I ),I e (C O ) Figure 4.12 EXIT chart of the proposed distributed turbo-like code, strategy B, for q = 4 users with optimal time allocation. Fast fading Rayleigh channel. R eff = q 2(q+1). The convergence threshold for q = 4 is γb sd = 0.35 db. the convergence threshold and by θs and θr the corresponding time allocation between the sources and the relay. Notice that given Rs and R eff, ρ p is fixed. In Table 4.5 we report the convergence thresholds for the case that the transmission time is allocated according to θs and θr. We also report the value of Rs. The same overall system rate R eff = q is assumed for all values of q. A significant gain with respect to equal 2(q+1) time allocation is observed. Notice that the gain significantly increases with increasing values of q. Also, the gap to capacity is within db, depending on the number of sources.

115 84 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS 4.7 Simulation Results In this section, we present the simulation results of the proposed system and we compare its performance with two reference systems. We evaluate the FER under equal time allocation between the sources and the relay. We also show the numerical results after optimizing the overall code parameters. We further show the performance for different number of users with equal coding rate, and we show how optimizing the time allocation improves the system performance with increasing number of users. Finally, we present numerical results over block fading channels and we show how the MARC system allows to gain diversity Simulation Parameters and Reference Systems We consider the R = 1/2 encoders defined in Section 4.4 for strategies A and B, punctured to higher rates whenever necessary. The extension of the proposed scheme to other constituent encoders at the sources, e.g., block codes or turbo codes, is straightforward. An S-random interleaver Π [DP95] and a maximum of fifteen decoding iterations are assumed. In all simulations the block length is k i = k = 96 bits and the overall system code rate is R eff = q, unless otherwise stated. The choice of the block length 2(1+q) k i = k = 96 bits is due to the fact that in sensor networks, the application highlighted for this work, each sensor usually deals with a small amount of information since a long block size would entail a high delay. In the sequel, we consider two settings for the relay network. In the first case, we assume that d sr = (1/4)d sd and d rd = (3/4)d sd (Assumption A3: the relay is closer to the sources than to the relay). In the second setup, we consider that the relay is positioned at half distance between the sources and the relay (d sr = (1/2)d sd and d rd = (1/2)d sd ).AsshowninSection , thislattercasecorrespondstotheposition that achieves the highest rate. For comparison purposes, we consider the non-cooperation scenario as the reference scenario. For fair comparison, we assume that each source transmits with a rate 1/3 which corresponds to the effective rate for two sources and with rate 1/2 since the effective rate tends to R eff = 1/2 for increasing q. We consider two non-cooperative systems: in the first system, each source encodes its information with a convolutional codes and in the second system turbo codes are used at the sources Results for Equal Time Allocation In Figure 4.13 and Figure 4.14 we give FER results for strategies A and B with equal time allocation for several numbers of users over a Rayleigh fast fading channel as a function of γ b sd expressed in db. Here, we assume d sr = (1/4)d sd and d rd = (3/4)d sd. We recall that the amount of information transmitted by the relay can be controlled by parameters J and ρ p for strategy A and B, respectively. We consider R i = R s = 1/2.

116 4.7. SIMULATION RESULTS FER γ b sd [db] q=2 q=8 q=20 q=50 No Coop CC R=1/2 No Coop CC R=1/3 No Coop TC R=1/3 No Coop TC R=1/2 Figure 4.13 FER curves for the distributed SCC using strategy A(filled markers) and B (empty markers) for q = 2,8,20 and 50 sources and equal time allocation q over Rayleigh fast fading channel. R i = R s = 1/2, R eff = 2(1+q).d sr = (1/4)d sd and d rd = (3/4)d sd. k i = k = 96 bits, 15 iterations. CC=convolutional code and TC=turbo code. Thus, to achieve R eff = q 2(1+q), J = q and ρ p = 1/q (see Section 4.2). From Figures 4.13 and Figure 4.14, we can notice that both strategies A and B perform similarly. While the block length k is very short the overall distributed SCCs turn out to be very powerful. Very low error rates are achieved for all values of q. Note that the curves shift to the right with increasing number of sources, since the effective code rate is higher. Note also that the curves get closer to the predicted convergence thresholds for increasing values of q. This result was expected, since the interleaver length, and therefore the block length, of the overall SCC increases with the number of sources. The proposed distributed SCCs show a significant gain with respect to the noncooperation scenario where convolutional codes are used at each source. It also outperforms the non-cooperation scheme where a turbo code is used at the sources even for a very large number of sources (q = 100). Due to the short block length, the non-cooperation curve using turbo codes at the sources shows a very shallow slope. In contrast, the proposed distributed SCC is able to attain much lower error rates for the same block length, since the overall code distributed over the sources and the relay is very powerful. In Figure 4.15, we give FER curves results for the two settings mentioned in Section for q = 2 and 4. From Figure 4.15, we observe the following: When the relay is at half distance between the sources and the destination better

117 86 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS FER γ b sd [db] q=4 q=16 q=30 q=100 No Coop CC R=1/2 No Coop CC R=1/3 No Coop TC R=1/3 No Coop TC R=1/2 Figure 4.14 FER curves for the distributed SCC using strategy A(filled markers) and B (empty markers) for q = 4,16,30 and 100 sources and equal time allocation q over Rayleigh fast fading channel. R i = R s = 1/2, R eff = 2(1+q). d sr = (1/4)d sd and d rd = (3/4)d sd. k i = k = 96 bits, 15 iterations. CC=convolutional code and TC=turbo code. performance is achieved in the waterfall region. An error floor is observed between FER 10 4 and 10 5 for d sr = (1/2)d sd and d rd = (1/2)d sd. This is due to an error propagation phenomenon at the relay. On the other hand, at FER=10 6 the floor is not yet observed for d sr = (1/4)d sd and d rd = (3/4)d sd. Inthesequel,wewillalwaysassumed sr = (1/4)d sd andd rd = (3/4)d sd,unlessotherwise stated. In Figure 4.16, we plot the FER curves for the distributed coding scheme working as a PCC (i.e., the relay estimates and encodes u i instead of x i, Section 4.3.2). A slight gain is observed in the waterfall region with respect to the distributed SCC. However, the distributed PCC suffers from an error floor between FER 10 4 and 10 5 even when the relay is closer to the sources, due to its poorer minimum distance Results for Optimal Time Allocation In Figure 4.17 we compare equal time allocation and optimal time allocation according to θs and θr (see Section 4.6.2) for strategy B for q = 20 and q = 100 sources. The overall system rate is R eff = q for both cases. For optimal time allocation, this 2(1+q) corresponds to R i = R s = 0.8,R I = 1.46 and R i = R s = 0.8,R I = 1.63 for q = 20

118 4.7. SIMULATION RESULTS q=2,d sr/d sd=1/2 q=2,d sr/d sd=1/4 q=4, d sr/d sd=1/2 q=4, d sr/d sd=1/ FER γ b sd [db] Figure 4.15 FER curves of the distributed SCC for two settings: d sr = (1/4)d sd and d sr = (1/2)d sd. R eff = q 2(1+q), k i = k = 96 bits, 15 iterations, fast fading channel. For d sr = (1/2)d sd, an error floor is observed between FER 10 4 and q=20 SCC q=100 SCC q=20 PCC q=100 PCC 10-2 FER γ b sd [db] Figure 4.16 FER curves of the distributed SCC with respect to the distributed q PCC, R eff = 2(1+q). k i = k = 96 bits, 15 iterations, fast fading channel. The distributed PCC suffers from an error floor between FER 10 4 and and q = 100, respectively. An improvement around 2 db and 4 db is achieved by

119 88 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS q=20, θs eq q=100, θs eq q=20, θ * s q=100, θ * s 10-2 FER γ b sd Figure 4.17 FER curves for the distributed SCC using strategy B for q = 20 and 100 sources over Rayleigh fast fading channel, for optimal (illed markers) and equal (empty markers) time allocation. R eff = q 2(1+q). k i = k = 96 bits, 15 iterations. optimal time allocation with respect to equal time allocation for q = 20 and q = 100, respectively. Note that the curves for q = 100 and q = 20 cross each other. While the curve for q = 100 converges a bit later (see Table 4.3) it decays more rapidly due to a larger inverleaver size Results for Equal Coding Rate Until now, we have considered an overall code rate depending on the number of users (R eff = q ). In this section, we consider a fixed code rate for different number of 2(q+1) users and we study the system behavior under both equal and optimal time allocation. Figure 4.18 depicts the FER curves of the proposed strategy B scheme with constant R eff = 1/3 and equal time allocation for several number of users (q = 2,4,20 and 100). Under equal time allocation assumption, the rate R s is given by R s = R eff (q + 1)/q. As shown in Figure 4.18, increasing q leads to a degradation in the performance of the proposed system. Figure 4.19 depicts the FER curves of the proposed distributed SCC (strategy B) with constant R eff = 1/3 and time allocation optimized by means of EXIT charts as explained in Section 4.6, for q = 2,4,20 and 100. The outer code rate R s is also chosen by means of EXIT charts. Since the global rate R eff is equal to 1/3, the outer rate R s must satisfy R s 2/3. Hence, while searching for the optimal pair (R s,r I ) which maximizes the convergence threshold as done Section 4.6, we limit R s to the set

120 4.7. SIMULATION RESULTS FER q=2 q=4 q=20 q=100 no coop. R=1/ γ b sd Figure 4.18 FER curves for the distributed SCC using strategy B for q = 2,4,20 and 100 sources over Rayleigh fast fading channel for a fixed rate R eff = 1/3 and equal time allocation. k i = k = 96 bits, 15 iterations. {0.5,0.52,...,0.66}. For q = 2,4,20 and 100, we obtain an optimal R s equal to 2/3. It is shown that for a given R eff increasing q improves performance. This is due to the fact that packing together more users, a stronger (larger interleaver) overall code is obtained Results over Block Fading Channels For the simulation results presented so far, we assumed channels with fast fading. In this section, we consider channels with less diversity where we assume that the fading coefficient is fixed for the frame duration. Figure 4.20 depicts the common frame error rate (CFER) of the proposed scheme over block fading channel for equal time allocation as a function of γsd b for q = 2,4 and 20 (filled markers). By CFER we mean the probability that a frame u i of at least one of the sources is not decoded correctly. The theoretical probability of outage computed as indicated in Section is also plotted for comparison (dashed lines). A combined coding and diversity gain is observed with respect to non cooperation. The proposed distributed code achieves second order diversity and performs within 2 5 db from the outage probability.

121 90 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS q=2 q=4 q=20 q= FER γ b sd Figure 4.19 FER curves for the distributed SCC using strategy B for q = 2,4,20 and 100 sources over Rayleigh fast fading channel for a fixed rate R eff = 1/3 and optimal time allocation. k i = k = 96 bits, 15 iterations Outage probability/ CFER q=2 q=4 q= γ b sd [db] Figure 4.20 CFER curves for the distributed SCC using strategy A (solid line, filled markers) and CFER curves for the non cooperation system (solid line, empty markers) for q = 2,4 and 20 sources over Rayleigh block fading channel. k i = k = 96 bits, 15 iterations. The outage probability curves are also reported (dashed lines).

122 4.8. DISTRIBUTED SERIALLY CONCATENATED CODES FOR UNRELIABLE SOURCE-TO-RELAY TRANSMISSION q=20 q=20 F p at decoders C i FER γ b sd [db] Figure 4.21 FER curves for the distributed SCC using strategy A for q = 20 sources over Rayleigh fast fading channel, d sr = (3/4)d sd. R eff = q 2(1+q). k i = k = 96 bits, 15 iterations. The solid curves correspond to the system with F pi used at the decoders and the dashed curves to classic decoding. 4.8 Distributed Serially Concatenated Codes for Unreliable Source-to-Relay Transmission In the previous sections, we have considered scenarios where the source-to-relay links are good enough so that the relay can decode the received message with few errors (assumption A3). In Section , we summarized the proposed approach in [Tho08] which considers noisy source-to-relay link for the relay channel. This approach was used for distributed parallel concatenated codes(dpcc) and was later applied to distributed serially concatenated codes (DSCC) in [STS09]. As explained in Section , the approach consists of a simple approximation of the optimal re-encoding procedure at the relay. The same approach can be used in our proposed scheme to overcome the error propagation at the relay. We assume that the transmitted codewords c i and the estimates ĉ i at the relay are in error with probability Pr(c i ĉ i ) = p i, under the assumption of memoryless source-to-relay channels. During the exchange of extrinsic information as described in Section 4.3.1, the LLRs L(ĉ) for the noisy estimates ĉ are converted into the LLRs L(c) for the actual codeword

123 92 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS bit c and vice versa by the transfer function F pi given in the following equation Numerical Results L out = F pi (L in ) ( ) (1 pi )exp(+l in /2)+p i exp( L in /2) = log p i exp(+l in /2)+(1 p i )exp( L in /2) i. (4.11) We compare the performance of our proposed system for noisy source-to-relay links when function F pi i = 1,...,q is used at the decoders and when classic decoding is performed as described in Section Again, we consider the same parameters of encoder C i as in Section 4.4, a block length k = 96 bits and an overall rate R eff = q/2(q +1). We consider that the relay is closer to the destination than to the sources and d sr = (3/4)d sd and d rd = (1/4)d sd. In Figure 4.21, we show the FER curves of the proposed system when F pi is used at decoder C 1 i and when it is not. A slight improvementisobservedwhenf pi isused.thebehaviorinthewaterfallregionremains the same. Indeed, this improvement is observed only in the floor, when errors occur at the relay, since we have chosen a setting where γ sr is not fixed to a certain value, i.e., γ sr is increasing with increased γ sd, therefore the impact of using F pi is observed at lower FER.

124 4.9. CONCLUSIONS Conclusions In this chapter, we considered wireless relay networks where multiple sources communicate with a single destination aided by a common relay. We assumed orthogonal scenarios. Orthogonality is obtained via TDMA. We proposed a flexible and simple distributed coding strategy for a multi-source scenario, capable to adjust in a very simple way to a different number of sources, as well as to code rate. The proposed distributed SCC achieves very low error rates even for a large number of sources and very short block lengths and a significant gain with respect to the non-cooperation case. In our approach, even for short block lengths (for instance k = 96 bits), the overall distributed turbo-like code turns out to be very powerful and very low error rates are achieved for different number of users (q 2). This is due to two issues: first, the information from all sources is combined and interleaved by a single interleaver prior to encoding by the relay. This allows achieving both diversity gain and interleaving gain. Second, thanks to the presence of multiple sources we can construct a long, therefore, powerful overall code. The proposed DSCC fits very well for applications such as sensor networks. In sensor networks, each sensor deals with a small amount of information. Previously proposed solutions as in [HD06] require a long block size, and that would entail a high delay, which is not acceptable in some applications. Our solution solves this problem since, as already explained, it offers good performance for short block lengths. Furthermore, in our proposal the amount of redundancy transmitted by the relay can be easily adjusted according to the number of sources, error rate requirements, overall system rate, optimal time allocation, and/or power constraints. Given the number of users q and the overall system rate R eff, i.e., the total information transmitted, our proposal allows to optimize the time allocation of the sources and the relay (i.e. the amount of information transmitted by the sources and by the relay) to achieve the best performance in a simple way. This is done by optimizing parameter J of the SPC for strategy A and the permeability ratio ρ for strategy B. Indeed, by means of an EXIT chart analysis, we can search for the optimal parameter which minimizes the convergence threshold. A similar scenario has been considered in [PGA10], where each source encodes its own information using the same block code. The relay decodes the codewords from the sources, places them in a matrix and then re-encodes the columns using another linear block code. The overall scheme can be regarded as a turbo product code. Significant performance gains with respect to the non-cooperation case are achieved. However, the scheme in [PGA10] presents several drawbacks. First, it lacks in flexibility. For instance, changing the number of sources requires the use of a different block code at the relay. Our proposed scheme provides a high flexibility in terms of code rate, number of users, throughput and error protection level with respect to the approach in [PGA10]. Furthermore, the extension to multiple destinations and to multiple relays is

125 94 CHAPTER 4. DISTRIBUTED TURBO-LIKE CODES FOR MULTIUSER COOPERATIVE SCENARIOS straightforward. Our detailed contributions in this chapter are the following: We proposed a distributed turbo-like code for a relay wireless network where multiple sources transmit to a destination with the help of a common relay. The relay uses a decode-and-forward strategy and operates in half-duplex mode. Two different encoding strategies are used at the relay. We presented the strategy we opted for in order to optimize the performance in terms of error floor and convergence. The encoder polynomials were chosen to lead to a good error floor. Then, we optimized the parameters J and ρ p according to other parameters, e.g., to optimize the achievable rate. We presented theoretical analysis of our system in terms of achievable rates and outage probabilities. Furthermore, we investigated how to allocate the transmission time between the sources and the relay and gave a closed-form expression of the optimal time allocation parameter which maximizes the achievable rates. We used EXIT charts to analyze the convergence behavior of the overall system and also as a tool to optimize the DSCC parameters. We considered the case when the transmission to the relay is not reliable. For this, we applied the same approach proposed in [Tho08, STS09] where we approximated the optimal re-encoding procedure at the relay to overcome the error propagation at the relay. In the scenario where TDMA is considered, the relay has to wait for q time slots. This delay is not suitable for some applications and can be mitigated by considering non-orthogonal scenario, where all sources transmit simultaneously. In the next chapter, we will consider non-orthogonal scenarios, and present the modifications applied to our proposed system for multiuser detection.

126 CHAPTER 5 Multi-User Scenario with Multiple-Access Interference In the previous chapter, we have considered scenarios with TDMA. For delay sensitive applications (e.g., speech and video transmission), non-orthogonal schemes where several sources are allocated the same bandwidth and time slot are more advantageous. Motivated by the fact that significant amount of work has been conducted for relay networks under the assumption of orthogonal links while few works have considered scenarios where severals sources transmit simultaneously, we consider in this chapter scenarios with multiple-access interference. A notable work [ZD05] considered a nonorthogonal scenario where a single source and a relay transmit simultaneously to a common destination. A turbo decoding scheme for relay systems together with iterative decoding were designed. In[ZD05], the source node sends coded information bits to both the relay and the destination, and the relay simultaneously forwards its estimate of the previous coded block to the destination after decoding and re-encoding. Thus, the destination receives a superposition of the codewords and uses iterative decoding to estimate the transmitted messages. The decoding in [ZD05] operates over all the transmitted blocks jointly. This coding/decoding scheme was also extended to MIMO relay systems. Since the receiver treats all the transmitted block jointly, this scheme implies a delay, therefore the extension to multiple sources scenarios is not straightforward. In this chapter, we consider the multi-source relay network of Chapter 4 where multiple sources transmit to a destination with the help of a relay with simultaneous multiple-access. As discussed in Chapter 2, several transmitting approaches can be used to deal with multiple-access interference at the destination, such as CDMA 95

127 96 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE [LV89] and IDMA [PLWL03a]. As explained in Chapter 2 (Section 2.6.4), IDMA involves a spreading operation of the data as in CDMA and an interleaving operation. Separation between users is obtained by the use of a different interleaver for each user. The complexity of the IDMA receiver for q users is O(q) [PLWL03b, PLWL03a] while that of CDMA system is O(q 2 ) [WP99]. In our work, we consider the use of IDMA for multiuser detection. This chapter is divided into two sections. In Section 5.1, we first consider a halfduplex relay scenario where the transmission time is divided into two slots and in Section 5.2 we consider a full simultaneous multiple-access scenario, i.e., a full-duplex relay scenario. In the two-slot scenario, one slot is devoted for the sources transmission and the other slot for the relay transmission. In the full simultaneous multiple-access scenario, all the sources and the relay transmit simultaneously. The detailed organization of each section is as follows. In Section 5.1.1, we describe the system model and the channel model. In Sections and 5.1.3, we present the encoding strategies at the relay and we describe the iterative decoding performed at the destination for multiuser detection. Information theoretic analysis is presented in Section 5.1.4, where we first analyze the IDMA and then we give the achievable rates of the cooperative system under both equal and optimal time allocation between the sources and the relay. Numerical results are presented in Section For the full simultaneous multiple-access scenario, the system description, the decoding process and numerical results are presented in Sections 5.2.1, and 5.2.3, respectively. Parts of this chapter are published in [YG11]. 5.1 Distributed Serially Concatenated Codes for Half-Duplex Relay with Multiple-Access Interference System Description System Model We consider the same relay network as depicted in Figure 4.1 where q sources transmit to a destination with the help of a relay. We first consider that the relay operates in a half-duplex mode. The transmission time is divided into two time slots. The q sources transmit simultaneously over a single communication channel during the first time slot t 1, realizing a MAC. The relay receives a superposition of the signals from all sources during the first time slot and transmits its own parity during the second time slot t 2. The transmission time is illustrated in Figure 5.1. Since all sources are allocated the same transmission time, a multiuser detection is required at the destination and the relay in order to separate the different signals.

128 5.1. DISTRIBUTED SERIALLY CONCATENATED CODES FOR HALF-DUPLEX RELAY WITH MULTIPLE-ACCESS INTERFERENCE 97 Figure 5.1 The transmission time is divided into two slots: one time slot is allocated for the q sources transmission and the relay transmits in the second time slot. For multiuser detection, we use IDMA. Our choice is justified by the low cost receiver [PLWL03b, PLWL03a]. The reader is referred to Section for more details on this technique. At each source, an IDMA transmitter is used. As for the orthogonal scenario in Chapter 4, each source s i, i = 1,...,q, encodes information sequence u si of length k i by encoder C i, of rate R i, into codeword c si of length n i = k i /R i. The sequence c si is then spread by using a repetition code into sequence c s i of length n sp i = mn i, where m is the spreading factor. The code rate after spreading is denoted by R sp i = R i /m. Finally,eachsequencec s i isscrambledbyinterleaverπ i intotheso-calledchipsequence c s i. The sequence c s i is then modulated into sequence x si. The structure of the IDMA transmitter at each source s i is depicted in Figure Due to the broadcast nature of the wireless channel the relay receives the superposition of noisy versions of the interleaved codewords from the different sources denoted by y r. After multiuser detection and decoding, the relay cooperates by transmitting its own parity sequence to the destination. For multiuser detection an IDMA receiver is used at the relay. The destination, on the other hand, receives first a superposition of the signals sent by the q sources. It then performs iterative multiuser detection followed by a joint decoding of the q sources information exploiting the additional redundancy sent by the relay in the second time slot Channel Model In this chapter, we maintain the same assumptions A1, A2, A3 and A4 as stated in Chapter 4 (Section 4.1.2). All sources transmit simultaneously during the first time slot. The received signals at the relay and at the destination, y sr and y sd, respectively, are the superposition of the chip sequences x si weighted by the channel coefficients

129 98 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE from the different sources, y sr = y sd = q 2γsr H si rx si +z sr, i=1 q 2γsd H si dx si +z sd. i=1 (5.1) H si r, H si d are diagonal matrices with Rayleigh fading channel coefficients in the main diagonal and zeros everywhere else. z sr and z sd are AWGN noise vectors with zeromean and unit-variance i.i.d. elements. After multiuser detection and decoding, the relay generates the parity sequence c r and cooperates with the sources by forwarding c r to the destination during the second time slot. The received observation at the destination is described as y rd = 2γ rd H rd x r +z rd. (5.2) where x r is the BPSK modulated sequence of the binary sequence c r Multiuser Detection at the Relay Since all sources transmit simultaneously, a multiuser detector at the relay is required to distinguish between signals from different users. We assume perfect synchronization. The relay uses an IDMA receiver that implements the chip-by-chip multiuser detection algorithm described in [PLWL06] (see Section ) to estimate codewords c i. The IDMA receiver, as depicted in Figure 2.22, consists of an ESE and q APP decoders C 1 i, corresponding to encoders C i. The ESE and decoders C 1 i exchange soft information on codewords c i in an iterative fashion. A decoding iteration consists of a single activation of the ESE and of the q decoders C 1 i, in this order. This process continues iteratively until a fixed maximum number of iterations is reached or an early stopping rule criterion is fulfilled Encoding Strategies at the Relay The relay receives a superposition of the noisy versions of the codewords c s i from the different sources. It decodes them and generates an estimate ĉ i of codewords c i. Decoding at the relay is performed by an IDMA receiver. The estimates ĉ i are then properly combined, interleaved into c and encoded using strategy A or strategy B into codeword c r. For more details on the encoding strategies A and B, the reader is referred to Section 4.2. Here, codeword c at the output of interleaver Π has length N = q i=1 n i. Therefore we have n r = N/R I and the effective overall system rate is R eff = K/N where now N = n sp i +n r. We recall that n sp and n r represent the number of symbols transmitted by the sources and the relay, respectively.

130 5.1. DISTRIBUTED SERIALLY CONCATENATED CODES FOR HALF-DUPLEX RELAY WITH MULTIPLE-ACCESS INTERFERENCE Decoding at the destination The destination receives the superposition of the signals from the q sources, y sd, and the noisy observation of the extra parity forwarded by the relay, y rd. It then estimates information words u i by exploiting jointly y sd and y rd. To this aim, an IDMA receiver is used to separate the signals of the q sources. Also, since extra parity is provided by the relay, an iterative exchange of information is also performed between decoders C 1 i and the decoder C 1 I of the relay, as described in Section The structure of the distributed SCC receiver with multiuser detection at the destination node is depicted in Figure 5.2. For the decoding scheduling, we define a global iteration an iteration between the IDMA receiver and decoder C 1 I, and a local iteration an iteration within the IDMA receiver. Here, we consider a single local iteration for each global iteration. We summarize the decoding scheduling in the following: The relay-to-destination channel metrics are fed to the inner decoder. The superposition of the q signals is received and treated by the ESE. The ESE uses the chip-by-chip detection algorithm and generates extrinsic information L e,ese ( c s i ) on c s i. This information is used after de-interleaving and de-spreading as a priori information at the input of decoders C 1 i, i = 1,...,q. Decoders C 1 i use the extrinsic information from the ESE to generate extrinsic information on codewords c si which will be passed to the ESE after proper spreading and interleaving. This completes one global iteration. Also, decoders C 1 i generate extrinsic information on codeword ĉ which is passed to the inner decoder C 1 The inner encoder C I is then decoded by using the extrinsic information on ĉ properly interleaved provided by the decoders of the sources as a priori information, and generates extrinsic information on c which will be used as a priori information (after de-interleaving) by the decoders of the sources at the next iteration. This completes a local iteration. The process repeats for a fixed maximum number of iterations or until it satisfies a certain stopping criterion. I.

131 100 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE ESE M U X Figure 5.2 IDMA receiver at the destination node. D E M U X

132 5.1. DISTRIBUTED SERIALLY CONCATENATED CODES FOR HALF-DUPLEX RELAY WITH MULTIPLE-ACCESS INTERFERENCE 101 Figure 5.3 Multiple-access channel with q layers Information Theoretic Limits We compute the achievable rates for the proposed scheme for a multiuser interference scenario with IDMA. As explained before, the transmission time is divided into two slots.inthefirsttimeslot,theq sourcestransmitsimultaneouslyrealizingamacatthe destination and the relay transmits in the second time slot. We first give the achievable rates by the IDMA system with q sources and later we compute the achievable rates of the overall system Channel Capacity of Multiple-Access Channel with q Layers In this section, we compute the channel capacity of a binary multiple-access channel with q layers assuming equal transmission rates per layer(as done in IDMA) and perfect successive interference cancellation following the approach in [HS06]. We consider a general multiple-access scenario which consists of a multiple-access channel with q layers as depicted in Figure 5.3. The block C i includes the encoder, the mapper and the interleaver. The received sequence is denoted by y = q H i x i +z. (5.3) i=1 Let k i be the length of the information sequence u i, n the length of codeword x i and R i = k i /n the transmission rate of the i-th layer. The overall transmission rate or the sum rate is given by q R = R i (5.4) and the overall received power by i=1 P = q P i (5.5) i=1 wherep i denotestheaveragereceivedpowerperlayer.wedefinen z asthenoisepower.

133 102 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE At the receiver, we consider perfect successive interference cancellation which is optimal in the sense of maximizing the overall channel capacity. We mean by perfect that error propagation is neglected (genie-aided detection). Without loss of generality, we assume that P 1 P 2... P q. (5.6) In successive interference cancellation, the strongest layer is detected first. The first layer can be decoded reliably if ( ) P 1 R 1 C N z + q j=2 P. (5.7) j Given the first layer, the detection of the second layer is done subsequently. The second layer is decoded reliably as well if ( ) P 2 R 2 C N z + q j=3 P. (5.8) j For layer i, the same principle is applied ( ) P i R i C N z + q j=i+1 P. (5.9) j The sum rate is maximized given the constraints in (5.5) and (5.6). We assume that R 1 = R 2 =... = R q = R/q which is the case in IDMA systems, i.e., the same encoder is used for all users or layers. Therefore, ( ) ( ) ( ) P 1 C N z + P 2 q j=2 P = C j N z + P i q j=3 P =... = C j N z + q j=i+1 P j ) (5.10) Hence, P 1 N z + q j=2 P j = =... = C ( Pq P 2 N z + q j=3 P j N z =... = P i N z + q j=i+1 P j =... = P q N z (5.11) Equation (5.11) is solved by starting with the weakest layer. Solving the equalities in (5.11) gives the following achievable sum rate ( ) q q ( P N R = R i = C z )f i (α) 1+ q j=i+1 (, (5.12) P N z )f j (α) i=1 i=1 where α = ( 1+( P )1 q ) N z (5.13)

134 5.1. DISTRIBUTED SERIALLY CONCATENATED CODES FOR HALF-DUPLEX RELAY WITH MULTIPLE-ACCESS INTERFERENCE q=1 q=2 q=3 q=4 Gaussian Inputs C in bit/channel use γ=p/n [db] Figure 5.4 Channel capacity of a binary multiple-access AWGN channel with q layers assuming equal transmission rates per layer as done in IDMA and perfect successive interference cancellation. and f k (α) = 1 k 1 l=0 αl + q k l=1, k = i or j. (5.14) 1 α l In Figure 5.4, we plot the channel capacity of a binary multiple-access AWGN channel for different values of q (q = 1,2,3 and 4) assuming equal transmission rate per layer and perfect successive interference cancellation. BPSK modulation is considered. As a reference, we also plot the channel capacity of an AWGN channel with Gaussian inputs Achievable Rates over the MARC Let k i,n sp i,n r and N be as defined in Section and Section We define the rateforsources i asr i = k i /N inbitsperchanneluse.theinformationoftheq sources s 1,...,s q can be decoded reliably at the destination if the following inequalities hold qk i n sp i C MUD(γ sr ) qk i n sp i C MUD(γ sd )+n r C(γ rd ) (5.15) where C MUD denotes the sum capacity of the MAC corresponding to the q sources s 1,...,s q. We define the time allocation parameters θ s = n sp i /N and θ r = n r /N for the q sources and the relay, respectively. Also, θ s +θ r = 1. Dividing by N in both sides of

135 104 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE Table 5.1 Minimum values of γsd b time allocation achieved over fast fading channel with equal γ b min,eq q = 2,m = 2 q = 4,m = 4 q = 8,m = 8 q = 12,m = 8 q = 16,m = db db db db db the inequalities (5.15) we obtain qr i θ s C MUD (γ sr ), qr i θ s C MUD (γ sd )+θ r C(γ rd ). (5.16) We compute C MUD following the approach in [HS06] assuming BPSK modulation. As shown in Section , C MUD is given by C MUD ( P N z ) = ( ) q ( P N C z )f i (α) 1+ q j=i+1 ( P N z )f j (α) i=1 where α and f i (α) are defined in Section (5.17) Achievable Rates with Equal Time Allocation We first consider equal time allocation between the q sources and the relay, i.e., θ s = θ r = 1/2. Under the assumption that all sources transmit at the same rate (R i = R s i), the achievable rates R i, i = 1,...q, are given by { 1 R i = R s = min 2q C MUD(γ sr ), 1 2q C MUD(γ sd )+ 1 } 2q C(γ rd). (5.18) The sum rate of the overall system is given by R eff = qr s. In Table 5.1 we report the minimum value of γsd b (γb min,eq) such that a system rate R eff = q is achieved over Rayleigh fast fading channel. In the computation, we assumed d sr = (1/4)d sd and d rd = (3/4)d sd 4m Achievable Rates with Optimal time allocation Again, the transmission time can be optimally allocated between the q sources and the relay in order to maximize the achievable rate. The optimal time allocation is chosen such that the rate R s is maximized. θ opt s = argmaxr s subject to θ r = 1 θ s. (5.19) We proceed in the same manner as done in Section The optimal time allocation θs opt is given by θ opt s = C(γ rd ) C(γ rd )+C MUD (γ sr ) C MUD (γ sd ), (5.20)

136 5.1. DISTRIBUTED SERIALLY CONCATENATED CODES FOR HALF-DUPLEX RELAY WITH MULTIPLE-ACCESS INTERFERENCE 105 Table 5.2 Minimum values of γsd b achieved over fast fading channel with optimal time allocation θ opt s θ opt r γ b min,opt q = 2, m = db q = 4, m = db q = 8, m = db q = 12, m = db q = 16, m = db while the achievable rates R i are given by R i = R s = 1 q C(γ rd )C MUD (γ sr ) C(γ rd )+C MUD (γ sr ) C MUD (γ sd ). (5.21) The rate of the overall system (sum rate) can be written as R eff = qr s = C(γ rd )C MUD (γ sr ) C(γ rd )+C MUD (γ sr ) C MUD (γ sd ). (5.22) In Table 5.2 we report the optimal time allocation parameters θs opt minimum values of γsd b (γb min,opt) such that a system rate R eff = q 4m and θr opt and the is achieved over Rayleigh fast fading channel for different values of q and m. An improvement of 0.8 to 1.4 db with respect to equal time allocation is observed. From the values of θs opt in Table 5.2 we obtain that for R eff = q, the optimal rate R 4m i for the sources is greater than 1, which does not make sense. For instance for q = 2, R i = In order to optimize the time allocation in such cases, i.e., when analytical results give unfeasible code parameters (R i ), we can use EXIT charts as done in Section Simulation Results The performance of the proposed scheme in a non-orthogonal scenario is evaluated through simulations. For strategies A and B, the 4-state, rate-1/2, feedforward convolutional encoder with generator polynomials (5,7) 8 is used at each source, and the 4-state, rate-1, recursive convolutional encoder with generator polynomial (3/7) 8 is used for C e. An S-random interleaver Π [DP95] is used at the relay prior to encoding. Also, a different random interleaver π i is used for each user, and different spreading factors m are considered for different values of q. We also assume that d sr = (1/4)d sd and d rd = (3/4)d sd. A block of length k i = k = 96 bits is considered and a maximum of thirty iterations is performed. In Figure 5.5 we give FER curves for the multi-source scenario with non-orthogonal channels for q = 2,4,8 sources and Rayleigh fast fading. Strategy A is considered at the relay and equal time allocation is assumed. Furthermore, R i = R s = 1/2, thereby R eff = q. A gain is observed with respect to non-cooperation. For instance, for q = 8 4m sources and m = 8 a gain around 5 db is obtained at FER=10 3.

137 106 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE q=2, m=2 q=4, m=4 q=8, m= FER γ b sd [db] Figure 5.5 FER curves, non-cooperation scheme (empty markers), cooperation scheme with strategy A (filled markers), with q = 2, 4, 8 sources, over fast fading channel. R i = R s = 1/2, R eff = q 4m. k i = k = 96 bits, 30 iterations. Figure 5.6 shows the FER curves of the proposed system when the relay encodes using strategy B and q = 12 and 16. Strategy B allows for a finer control of the redundancy transmitted by the relay. A significant gain is observed with respect to the non-cooperation system. For instance, for q = 16 sources a gain of almost 3.5 db is observed at FER=10 4 with respect to non-cooperation. Notice that in Figure 5.6, unlike in Figure 5.5, a gap is observed between the curves because we are considering the same spreading factor, i.e., m = 8 for q = 12 and 16 sources. 5.2 Full Simultaneous Multiple-Access System System Description In this section, we consider a full simultaneous multiple-access scenario. In this scenario all sources and the relay are allocated the same transmission time and the same bandwidth. This strategy with full multiple-access requires a full-duplex relay. Figure 5.7 shows the corresponding transmission time allocated to the q sources and the relay transmit simultaneously. At the sources, the encoding remains the same as described in Section On

138 5.2. FULL SIMULTANEOUS MULTIPLE-ACCESS SYSTEM q=12, m=8 q=16, m= FER γ b sd [db] Figure 5.6 FER curves, non-cooperation scheme (empty markers), cooperation scheme with strategy B (filled markers), with q = 12 and 16 sources, over fast fading channel. R i = R s = 1/2, R eff = q 4m. k i = k = 96 bits, 30 iterations. the other hand, the encoding strategy at the relay differs from the encoding presented in Section The block diagram of the encoding at the relay is depicted in Figure 5.8. Since the relay signal is superposed with the sources signals, an IDMA transmitter has to be used at the relay, i.e., a spreading code is added after encoder C I followed by an interleaver π r specific to the relay. After detection of the sources codewords, the relay combines the estimates ĉ si, and interleaves the resulting codeword ĉ into codeword c. The resulting codeword is then encoded into codeword c r using strategy A or strategy B as described in Section 4.2. Prior to forwarding, codeword c r is then spread by a repetition code of factor m into codeword c r and interleaved by interleaver π r specific to the relay into codeword c r. For the channel model, assumptions A1, A2, A3 and A4 are applied to this strategy. The received signals at the relay and the destination are respectively given by y sr = y = q 2γsr H si rx si +z sr, i=1 q 2γsd H si dx si + 2γ rd H rd x r +z. i=1 (5.23)

139 108 CHAPTER 5. MULTI-USER SCENARIO WITH MULTIPLE-ACCESS INTERFERENCE Figure 5.7 Transmission time allocation for simultaneous multiple-access. M U X Π Spreading Code AWGN Figure 5.8 IDMA transmitter at the relay: After encoding using strategy A or B, a spreading code followed by an interleaver is used at the relay. where x si and x r are the modulated sequences of the binary sequence c s i and c r, respectively, H si r, H si d and H rd are diagonal matrices with Rayleigh fading channel coefficients in the main diagonal and zeros everywhere else and z sr and z are AWGN noise vectors with zero-mean and unit-variance i.i.d. elements Decoding at the destination The destination receives the superposition of the signals from the q sources and the relay, y. An IDMA receiver is employed at the destination in order to separate the q+1 signals. The IDMA receiver at the destination is depicted in Figure 5.9. It consists of an corresponding to the q sources and to the relay, respectively. The decoding at the receiver is done by iterating between the ESE and the q + 1 decoders using the chip-by-chip detection algorithm described in Chapter 2, Section Also, since the relay cooperates by transmitting a new version of the information of the different sources, iterations are also performed between ESE and q +1 APP decoders C 1 i the outer decoders C 1 i i = 1,...,q and C 1 I corresponding to the source encoders and the inner decoder C 1 I corresponding to the relay encoder. The exchange of extrinsic information between the outer and the inner decoders is done as described in Section We define global and local iterations. A global iteration is completed when the ESE and the constituent decoders C 1 i exchange extrinsic information. A local iteration is completed when the outer decoder C 1 i and the