RELIABILITY-BASED HYBRID-ARQ USING CONVOLUTIONAL CODES

Transcription

1 RELIABILITY-BASED HYBRID-ARQ USING CONVOLUTIONAL CODES By ABHINAV ROONGTA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2005

2 Copyright 2005 by Abhinav Roongta

3 To my parents and my sister

4 ACKNOWLEDGMENTS First I would like to thank and express my sincere gratitude to my advisor, Dr. John M. Shea. This work would not have been possible without his expertise, hard work and patience. He guided me at each and every stage of my Ph.D. program and was always easily accessible. He read and revised all our conference papers and presentations and worked unlimited nights and weekends for our journal article. Besides being a great research advisor, I also wish to thank him for his excellent teaching in EEL and EEL. The efforts that he put in his teaching, in his lectures and creating questions for the exam, really amazed me right from day one of 5544 when he gave the Monte-Hall problem. I would also like to thank Dr. Tan Wong, Dr. Yuguang Fang and Dr. Richard Newman for providing valuable input at the time of my Ph.D. proposal defense. Dr. Richard Newman read this dissertation from cover to cover and provided detailed feedback for improving it. I would also like to thank all the students in our lab, NEB -. Thanks to Arun for helping me debug my code on several occasions and strengthening my belief that reliability-based hybrid ARQ is a practical solution; Jang-Wook for patiently answering my questions on jamming model and estimation; Deniz for giving me his LaTex templates and organizing the WING picnic; Sarva and Jianfeng for organizing the WING seminar. I would also like to thank Hongqiang Zhai for bringing me up to speed with network simulator (ns2). I also thank my friends Adrian and Brock for burning the midnight oil with me while coding adaptive signal processing algorithms in MATLAB. Together we managed to sail across the troubled waters of EEL. I wish to thank certain behind-the-scene people who directly or indirectly contributed towards this dissertation. I thank Linda Kahila and Shannon Chillingworth in iv

5 the ECE Graduate Student Services Office for advising on degree requirements, taking care of paper work and sending regular reminders regarding registration and fee payment deadlines. Thanks to them I never had to read the Graduate Student Handbook. Thanks to Janet Holman, our administrative secretary, for keeping the lab well stocked and doing the paper work for travel to conferences. I also thank all my non-ece friends and my current and past apartment-mates for making life fun. Thanks to Abhudaya and Nitin, my current apartment-mates, for giving me ride to the lab on weekends. Together we survived the hurricanes in the Gatorland. Finally, I would like to thank my parents, Santosh and Madhu Roongta, and my sister Aastha to whom I owe everything. I have become what I am because of their sacrifices, blessings and unconditional love and support. Thank you! v

6 TABLE OF CONTENTS page ACKNOWLEDGMENTS iv LIST OF TABLES viii LIST OF FIGURES ABSTRACT ix xi CHAPTER 1 INTRODUCTION Previous Work on Hybrid ARQ Objective Main Contributions Outline of This Dissertation RELIABILITY-BASED HYBRID ARQ FOR NON-FADING CHAN- NELS WITHOUT INTERFERENCE System Model RB-HARQ using Convolutional Codes without Puncturing RB-HARQ with Variable Redundancy and Smaller Request Packet RB-HARQ with RCPC Codes and Arithmetic Coding Error Probability Comparison of RB-HARQ with HARQ with RCPC codes Throughput Comparison of RB-HARQ with HARQ with RCPC codes RELIABILITY-BASED HYBRID ARQ FOR PARTIAL-TIME JAM- MING CHANNELS MAP Estimation Algorithms Maximum-Likelihood Estimation of Jammer Parameters Reliability-Based Hybrid ARQ Schemes Analysis of Probability of Packet Error for HARQ Size of retransmission-request packet Performance of Estimation Algorithm Performance Results Packet error probabilities vi

7 3.5.2 Throughput Results RELIABILITY-BASED HYBRID-ARQ FOR CSMA-CA-BASED WIRE- LESS NETWORKS Interference Modelling Non-Fading Channel Model Performance of Reliability-Based Hybrid-ARQ in CSMA-CA- Based Networks CONCLUSIONS AND DIRECTIONS FOR FUTURE WORK Conclusion Directions for Future Work REFERENCES BIOGRAPHICAL SKETCH vii

8 LIST OF TABLES Table page 4.1 Simulation parameters in ns Interference parameters obtained using simulation viii

9 LIST OF FIGURES Figure page 2.1 Probability of bit error by reliability rank for rate 1/2, (5,7) convolutional code System model for hybrid ARQ with convolutional codes Probability of bit error vs. Effective for three retransmissions of incremental redundancy each Reliability values for example packet of information bits Reliability values, after elimination and smoothing for example packet of information bits Average number of bit indices fedback ( ) and average number of information bits requested for retransmission ( ) vs. for RB- HARQ scheme Probability of bit error vs. Effective for RB-HARQ scheme with variable redundancy and reduced retransmission-request packet Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/ Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 4/ Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/ Performance comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate 2/ Throughput comparison of the proposed RB-HARQ scheme with the RCPC-HARQ scheme with initial code rate Communication scenario System model Two-state Markov model for jammer ix

10 3.4 Probability of miss and false alarm of jammed symbols when all jamming parameters must be estimated in comparison to when all jamming parameters are known at db Probability of packet error for RB-HARQ(J) with estimation of jamming parameters or perfect CSI, and = -3 db Probability of packet error for RB-HARQ(J), Type-I HARQ and retransmission of a random set of symbols, and db Probability of packet error for three retransmissions of RB-HARQ(J), and db Probability of packet error for different RB-HARQ schemes compared with Type-I HARQ and conventional HARQ, and = 0 db Probability of packet error for different RB-HARQ schemes, and db Probability of packet error for adaptive and fixed RB-HARQ, and = -3 db Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ, after 3 retransmissions at and db Throughput of adaptive RB-HARQ(R), RB-HARQ(J), Type-I HARQ and conventional (uniform) HARQ, and = db Throughput for RB-HARQ, Type-I HARQ and conventional (uniform) HARQ as a function of at db, db Probability density function of the normalized power of the interfering packet Effect of interference on probability of packet error for AWGN channel Throughput for Type-I HARQ with up to 2 retransmissions and Throughput for RB-HARQ and Type-I HARQ with up to 2 retransmissions and AWGN channel x

11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy RELIABILITY-BASED HYBRID-ARQ USING CONVOLUTIONAL CODES By Abhinav Roongta August 2005 Chair: John M. Shea Major Department: Electrical and Computer Engineering In this work we develop selective-retransmission hybrid-arq protocols for communication systems that use soft-input soft-output (SISO) decoders. The schemes that we propose are based on reliability-based hybrid-arq that use the estimated a posteriori probabilities at the output of the SISO decoder to adaptively determine the set of bits to be retransmitted in response to error detection. First we show the performance of the proposed scheme for nonfading additive white Gaussian noise channels without any interference. We begin by evaluating the performance of a simple reliability-based hybrid ARQ scheme that uses fixed rate convolutional codes in the forward channel and exploits their time-correlation properties to achieve smaller retransmission requests. Then we extend our work where rate-compatible punctured convolutional (RCPC) codes are used in the forward channel and arithmetic coding is used in the feedback channel. We compare the performance of the proposed scheme with the common approach to hybrid-arq that uses punctured convolutional codes. The results show that the proposed RB-HARQ scheme achieves better performance than a hybrid-arq scheme that uses only RCPC codes. xi

12 Next we extend our work to improve communication performance on partial-time jamming channels. For channels with partial-time jamming, we can extend our measure of reliability to incorporate not only a posteriori probability information but also estimates of the probability that a bit was jammed. We compare the performance of the proposed scheme with that of a conventional approach in which a predetermined set of bits is retransmitted in response to a packet failure. The results show that RB-HARQ schemes can achieve better performance than the conventional approach. Next we extend our work to wireless networks that use carrier sense multiple access with collision avoidance (CSMA-CA). We first propose a new channel model that considers the packet errors due to channel noise as well as those due to interference from simultaneous transmission by other nodes. The proposed channel model takes into account the fact that collisions may result in parts of a packet being corrupted while other parts are received without corruption. Therefore, the proposed channel model is more realistic than an AWGN channel model and can be used in a cross-layer design approach which considers combining ARQ at the data link layer and channel coding at the physical layer. We also investigate the performance of a RB-HARQ technique for CSMA-CA-based wireless networks. xii

13 CHAPTER 1 INTRODUCTION Automatic-repeat-request (ARQ) and forward-error-correction (FEC) are two basic techniques for controlling transmission errors in data communication systems [1,2]. Automaticrepeat-request schemes typically use a high-rate error-detecting code. They are simple and provide high system reliability. However, one severe drawback of ARQ systems is that their throughput efficiency falls rapidly with increasing channel-error rate. An FEC communication system uses a powerful error-correcting code to combat transmission errors. The throughput efficiency of such systems is maintained at a constant level (equal to the code rate) regardless of the channel error rate. The drawback of an FEC system is that it is difficult to achieve high system reliability and decoding is hard to implement. Thus, ARQ is often preferred over FEC for error control in data communication systems, such as packet-switching data networks and computer communication networks. Forward-errorcorrection is preferred over ARQ in communication systems where return channels are not available or retransmission is not possible for some reason. Hybrid-ARQ (HARQ) schemes that use a proper combination of ARQ and FEC can overcome the drawbacks of both ARQ and FEC schemes. Systems that use HARQ consist of an FEC subsystem contained within an ARQ system. The FEC subsystem reduces the frequency of retransmissions by correcting many common error patterns without retransmission, thus increasing the throughput of the system. When an uncorrectable error is detected, the ARQ system requests retransmission instead of passing the unreliably decoded message to the user. Thus HARQ systems provide higher reliability than an FEC system alone and higher throughput than the system with ARQ only. Hybrid-ARQ schemes are broadly classified into Type-I and Type-II hybrid-arq schemes. Type-I HARQ schemes 1

14 2 use a code designed for simultaneous error correction and error detection. Therefore, the codes used in such schemes require more parity bits than a code used only for error detection. This increases the overhead for each transmission. As a result, when the channel error rate is low, the type-i hybrid ARQ scheme has a lower throughput than its corresponding ARQ scheme. However, type-i HARQ schemes provide higher throughput than the corresponding ARQ scheme when channel error rate is high because HARQ scheme s errorcorrection capability reduces the frequency of retransmissions. Type-II HARQ schemes are based on the concept that the parity check bits for error correction are sent to the receiver only when they are needed. 1.1 Previous Work on Hybrid ARQ The concept of type-ii HARQ or the incremental-redundancy HARQ schemes was first introduced by Mandelbaum [3] and then extended by Metzner [4], Ancheta [5] and Lin and Yu [6]. In these schemes, a message is encoded using a code for error-detection only. If the receiver detects the presence of errors in a received codeword, it saves the erroneous message in a buffer and sends a NACK to the transmitter. The transmitter then transmits a block of parity-check bits formed based on the original message and an errorcorrecting and error-detecting code. When this parity block is received, it is used to correct the erroneous message stored in the buffer. In case the error correction is successful, the corrected message is delivered to the data sink. If the error correction is unsuccessful, the receiver requests a second retransmission, from the transmitter, which may be either the original codeword or again a parity block. Type-II HARQ scheme provides better performance than the type-i HARQ scheme if the code used for error correction and the retransmission strategy is properly chosen. Incremental-redundancy hybrid-arq schemes that use punctured convolutional codes and code combining were proposed by Hagenauer [7]. In these and other hybrid-arq schemes [1, 2], the set of bits to be transmitted in response to error detection is a predetermined part of the ARQ algorithm. For example, consider the

15 3 HARQ scheme proposed by Hagenauer [7] in which rate-compatible punctured convolutional (RCPC) codes are used. In this scheme if the higher rate codes are not sufficiently powerful to decode channel errors, a predetermined subset of the bits that were previously punctured is transmitted in order to decrease the code rate. Automatic-repeat-request has also been considered to improve the performance of wireless communications in the presence of interference. Hostile jamming can severely disrupt wireless communications. The typical responses to such disruptions are retransmissions through ARQ, ARQ with adaptation of the signaling parameters [8-12], and adaptation in the network layer [13-17]. The performance of Type-I hybrid-arq protocols in a slotted direct-sequence code-division multiple-access network operating in a hostile jamming environment was studied by Hanratty and Stuber [18]. The effect of jamming on throughput of HARQ protocol was also studied by Feldman and Levannier et al. [19, 20]. Wilkins and Pursley [11] evaluated the performance of an adaptive rate coding system for channels with Rayleigh fading, partial-band interference, and thermal noise. It was shown that adaptive-rate coding systems provide significantly higher throughput than systems that use fixed-rate coding. This is because adaptive-rate coding systems use a highrate code, which gives high throughput rate, when channel conditions are good, and use a low-rate code only when necessary to combat a large amount of interference. Pursley and Wilkins [10] showed that it is beneficial to be able to change both the transmission power and the code rate in a slow-frequency hopping communication system. It was suggested that the code rate should be adapted based on the jammer parameters while the power level should be adapted based on signal-to-noise ratio. Most of the previous work identifies that adaptation is the key to responding to jamming. However, in each of these works, traditional ARQ is assumed. Although traditional ARQ is adaptive in the sense that retransmissions only occur when a packet is in error, it is non-adaptive in the sense that the response to a packet error is fixed: the entire packet should be retransmitted. Even if hybrid-arq is used, the response neither adapts to the

16 4 reliability of the received packet nor to the set of symbols that was jammed. A reliabilitybased hybrid ARQ (RB-HARQ) algorithm that is truly adaptive was proposed by Shea [21]. In RB-HARQ, soft-input soft-output decoders are used to identify which bits in a received packet are unreliable, and retransmissions are requested for only those unreliable bits. By requesting information for the unreliable bits, the performance of the decoder can improve more quickly than if a fixed HARQ scheme is used. The performance of RB-HARQ using turbo codes and convolutional codes over AWGN channel was shown by Kim and Shea [22] and Roongta and Shea [23], respectively. Another RB-HARQ scheme that uses received packet reliability to optimize throughput over static and time-varying channels was independently proposed by Tripathi et al. [24]. All of the previous work on RB-HARQ [21-25] uses the magnitude of the log a posteriori probability ( -APP) ratio computed by the maximum a posteriori (MAP) [26] algorithm to identify the unreliable bits. 1.2 Objective The objective of this work is to develop selective-retransmission hybrid-arq protocols that will efficiently use the soft-output available at the decoder and achieve better performance than the conventional HARQ schemes considered in different research studies [3-20]. These protocols are aimed at improving the performance of wireless communication systems that suffer from hostile interference. However, the protocols that we develop are general enough that they can be used for any communication system that uses soft-input soft-output (SISO) decoders. 1.3 Main Contributions In this work we propose and evaluate the performance of selective-retransmission hybrid-arq protocols that significantly improve the performance of communication systems that use soft-input soft-output decoders. In all of the previous work that uses ARQ [3-20], the set of bits to be retransmitted is not adapted to the set of bits that are likely to be in error. The work presented here is unique in this sense. The proposed work uses a MAP

17 decoding algorithm to identify bits that are likely to be in error. For communication systems that suffer from hostile jamming, the proposed work uses iterative MAP algorithms to estimate the probabilities that a bit is jammed and in error. The retransmissions in the proposed hybrid-arq schemes are adapted to the the set of bits that are likely to be in error or jammed. The main contributions of this work are: We propose reliability-based hybrid-arq (RB-HARQ) for nonfading AWGN channels without any interference. The proposed scheme adapts the retransmission to the set of unreliable bits identified using the - APP for each information bit, uses rate-compatible punctured convolutional (RCPC) codes, with or without puncturing, in the forward channel, achieves small retransmission request packets by 5 using simple arithmetic coding on the feedback channel, or using the time correlation properties of convolutional codes. adapts the size of retransmission to the channel conditions. This also We develop RB-HARQ to improve communication performance in a hostile jamming environment. The proposed scheme uses the -APP of the information bits and the -APP ratio of jammer state to identify the unreliable bits, uses iterative MAP algorithms to estimate the probability that each bit is jammed as well as the reliability of each bit, adapts the retransmission based on the output of these MAP algorithms, and uses optimal run-length arithmetic coding or a suboptimal but less complex source coding to compress the retransmission request packet. We provide a performance comparison of the proposed RB-HARQ schemes with the conventional HARQ in which a predetermined set of bits is retransmitted. We propose a new channel model for ad-hoc wireless networks that not only considers errors due to channel noise but also considers errors due to interference caused by simultaneous transmission by other nodes.

18 We propose a RB-HARQ technique for wireless networks that use carrier-sense multiple access with collision avoidance (CSMA-CA) and investigate the performance of the proposed technique. 1.4 Outline of This Dissertation This dissertation is organized as follows. Chapter 1 gives the introduction to the work presented in this report. Chapter 2 presents the proposed work and evaluates its performance for nonfading additive white Gaussian noise channels without any interference. Chapter 3 presents the work for partial-time jamming channels. Chapter 4 presents a new channel model for ad-hoc wireless networks which can be used to design efficient HARQ protocols. In Chapter 5 we present conclusions and directions for future work. 6

19 CHAPTER 2 RELIABILITY-BASED HYBRID ARQ FOR NON-FADING CHANNELS WITHOUT INTERFERENCE In this chapter, we propose and evaluate the performance of RB-HARQ techniques for nonfading AWGN channels without any interference. We also compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [7], which uses punctured convolutional codes. The RB-HARQ technique that we propose is motivated by an understanding of the decoding process and analysis of the error packets. We use the MAP algorithm [26] for the decoding of convolutional codes. For each information bit, the decoder computes the a posteriori probability ( -APP) ratio [27] as follows (2.1) where is the received codeword in noise. When the decoder fails to decode a packet correctly, it is because the decoder has failed to find soft-decision -APP values with the correct signs for some of the information bits in the packet. The bits that have soft-decision -APP values with incorrect signs result in errors at the decoder output. Analysis of error packets reveals that the decoder can use the -APP values to accurately identify the bits that prevent the packet from decoding correctly [21]. We refer to such bits as weak bits. To see this, consider a block of 1000 information bits encoded by a rate convolutional code with generator polynomials and for transmission over an additive white Gaussian noise (AWGN) channel. For each error packet, rank the bits at the output of the convolutional decoder by the magnitude of their soft-decision -APP values. The bit with the smallest soft-output is considered the least reliable (0), and the bit with the largest soft-output is considered most reliable (999). The probability of error for each bit by rank is shown in Figure 2.1. These results indicate that 7

20 Probability bit is in error E b / N o = 0 db E b / N o = 1 db Bit reliability (0=least reliable) Figure 2.1: Probability of bit error by reliability rank for rate 1/2, (5,7) convolutional code. the least reliable bits correspond to errors about of the time, while very reliable bits are rarely in error. Thus the bits that have small -APPs are likely to be the weak bits. The performance of the decoder is likely to improve if additional information about the weak bits can be used to improve their soft-decision estimates. 2.1 System Model The system model for the work presented in this chapter is shown in Figure 2.2. The communication system consists of the source radio and the destination radio linked by a data channel through which a packet of information is to be delivered from to. Convolutional codes are used for encoding the data bits in. The encoded packet is then appropriately punctured to get the desired initial code rate. The resulting code bits are modulated using BPSK and then transmitted over an AWGN channel. The destination radio

21 9 u k Conv. Encoder Source Radio Puncture BPSK Modulator Data Channel Destination Radio Conv. Decoder u k Error Detector S Source Decoder Feedback Channel Source Encoder D Figure 2.2: System model for hybrid ARQ with convolutional codes. attempts to decode the packet and sends a retransmission request through the feedback channel if an error is detected. uses the magnitudes of the -APPs to identify the leastreliable bits and constructs the retransmission-request packet, which contains a list of such bits. The source encoder in the destination radio is used to compress the retransmissionrequest packet. The source radio decodes the encoded retransmission-request packet and then retransmits the code bits corresponding to those requested information bits. To further clarify, for any requested information bit transmits all the corresponding code bits irrespective of whether they were punctured in the initial transmission. Noisy versions of the retransmitted code bits are received at and are added to any previously received values of the same code bits. In our study, we assume perfect error detection and the presence of a highly reliable feedback channel from to. Note that the source encoder in and source decoder in are only used for retransmission-request packets transmitted over the feedback channel. 2.2 RB-HARQ using Convolutional Codes without Puncturing We first investigate the performance of the RB-HARQ scheme without puncturing and without any source coding. We will use the results to determine the relative degradation of the approach to compressing the request packet, as discussed in the next section. For all the results in this section, the code used for transmission from to is a rate 1/2, constraint length convolutional code with generator polynomials (in octal) 554 and 744. These results also apply if the feedback channel has a high capacity so that a large

22 10 retransmission-request packet can be sent from to. The source initially transmits the packet using a rate 1/2 convolutional code. If fails to decode the packet correctly, it sends a retransmission-request packet containing a list of the positions of the leastreliable information bits. In the work by Kim and Shea [22], responds to the request packet by retransmitting the information bits. However, the code in their work [22] is a systematic turbo code, whereas the code we consider in this section is a nonsystematic convolutional code. Thus, for these results, retransmits the two code bits corresponding to each of the positions identified by. To further clarify, is using the reliability of the information bits to identify weak sections in the code trellis and then requests new code information for those trellis sections. The received code symbols are combined with all previously received copies of those symbols. For BPSK transmission over an AWGN channel, the soft-outputs for the symbols can be added together. For the results presented in this section, each packet consists of 1000 information bits. Each retransmission request consists of a list of 50 bit positions, and transmits 100 code bits in response to each request. This corresponds to incremental redundancy per retransmission. We consider the performance when the request and retransmission process can occur up to three times. Each retransmission effectively reduces the code rate and hence increases the at the receiver. We account for this additional received energy by defining the effective as the average at the receiver, taking into account the average number of incremental redundancy transmissions per packet. The results in Figure 2.3 show the probability of bit error for reliability-based hybrid-arq with the rate 1/2, constraint-length seven convolutional code. In Figure 2.3 we observe that to achieve a probability of bit error of less than, a system using RB-HARQ technique with three retransmissions of incremental redundancy each requires db lower than a system with no ARQ. Most of the performance has been gained after only two incremental transmissions, and the third transmission only improves performance by approximately

23 No ARQ After 1st retransmission After 2nd retransmission After 3rd retransmission Probability of bit error Effective E b / N o (db) Figure 2.3: Probability of bit error vs. Effective for three retransmissions of incremental redundancy each. 0.1 db. Further improvement in performance may be achieved by optimizing the number of bits retransmitted in each iteration. We note that for the technique presented in this section, the retransmission-request packet can be very large. Consider the following example. For a packet of information bits, each bit index can be represented by a ten-bit binary number. So, without any compression, the retransmission-request packet consisting of least-reliable bit indices, will consist of bits. Such a large retransmission-request packet will generally decrease the overall system throughput. In the next section, we present results for a variable redundancy RB-HARQ scheme which has a much smaller retransmission-request packet.

24 RB-HARQ with Variable Redundancy and Smaller Request Packet The RB-HARQ scheme that we present in this section has variable redundancy. As channel conditions improve, fewer bits are retransmitted. The scheme that we propose in here is based on two important observations during our simulations. The first observation, as shown in Figure 2.1, is that in any packet with errors, the bits that are in error have low reliability (magnitude of -APP) values. The second observation is that in any packet with errors, the error events (the bits that are in error) are correlated in time. The results in Figure 2.4 illustrate the reliability values for each bit in an example packet that was decoded in error as a function of the bit index (position in the packet). The packet size is information bits, and it was transmitted over an AWGN channel using the rate convolutional code with constraint length. The results in Figure 2.4 also indicate the bits that were in error. We observe from the figure that bits that are in error have low reliability values and occur in groups (time-correlated). There is one group of error bits around bit index and another group of error bits around bit index. Based on the two observations made above, we modify the RB-HARQ technique proposed earlier. The system model remains the same as in Figure 2.2. Whenever the destination radio fails to decode a packet correctly, it calculates a threshold based on the reliability values of the bits in that packet. Then it performs an operation in which all the reliabilities greater than operation, performs a operation as follows:! #" are made zero. Following the (2.2) In our study, the threshold is calculated as follows: %$ '& ( (2.3)

25 13 25 Reliability value Bits in error 20 Magnitude of log APP Bit index Figure 2.4: Reliability values for example packet of information bits. where $ is the minimum reliability value and the ( is the average reliability value of the packet in consideration. We were guided by the following considerations while selecting the threshold in (2.3): (i) The threshold calculation should be computationally simple. (ii) The threshold should be large enough so that it is greater than the least reliability value because the bits with low reliabilities are the ones that are likely to be in error. (iii) The threshold should be small enough that the size of retransmission request packet is small and the number of bits retransmitted is not very large. The operation was performed using a rectangular window of length as described by (2.2). Figure 2.5 shows the reliability values, after the and operations were performed, for the packet with errors shown in Figure 2.4. We observe in Figure 2.5 that there are windows (groups) of non-zero reliabilities in the entire packet.

26 The destination radio,, sends the first bit index and the last bit index, of each window, to. The source then retransmits the code bits, corresponding to all the information bits, in each of the window. Thus, the number of bit indices sent back from to is fewer than the number of information bits that are actually requested for retransmission. We define to be the average number of bit indices per retransmission-request packet sent from to. We also define to be the average number of information bits requested for retransmission for every packet in error. The results in Figure 2.6 show the above two quantities ( and ) at various values of the channel symbol energy-to-noise 14 density ratio ( ). We observe that a large reduction in the size of retransmissionrequest packet has been obtained. For example, at db the average number of bit indices per retransmission-request packet ( ) is bits requested per packet with errors ( ) is whereas the average number of information. At db, is and is. We note that in the RB-HARQ technique presented in the previous section, all the bit indices had to be fed back ( ) to the source radio. Thus we have obtained more than percent reduction in the size of the retransmission-request packet. The scheme presented in this section has variable redundancy compared to fixed redundancy in the previous section. By doing this we are able to take advantage of better channel conditions. As improves, we request fewer information bits and hence, fewer code bits are retransmitted. Hence, the redundancy decreases with increasing SNR, which leads to higher throughput. The results in Figure 2.7 show the probability of bit error for a system that uses RB- HARQ technique with variable redundancy and small retransmission-request packets. Figure 2.7 shows that to achieve a probability of bit error of less than, a system using the above ARQ technique requires db lower than a system with no ARQ. We note that this improvement in the system performance has been obtained by using a simple heuristic for calculation of threshold. System performance can be further improved by optimizing the threshold, packet size and the lenth and shape of the window used for the operation. The RB-HARQ scheme in this section performs about db worse

27 Reliability value Bits in error 1 Magnitude of log APP Bit index Figure 2.5: Reliability values, after elimination and smoothing for example packet of information bits. than the scheme in the previous section, but reduces the size of the retransmission-request packet by at least percent at all signal to noise ratio (SNR) values. 2.4 RB-HARQ with RCPC Codes and Arithmetic Coding In this section we evaluate the performance of a RB-HARQ scheme that uses ratecompatible punctured convolutional (RCPC) codes in the forward channel and arithmetic coding in the feedback link. First we compare the performance of the proposed technique with a system without ARQ. Then in section we compare the performance of the proposed technique with that of the HARQ technique that uses only RCPC codes. The performance is evaluated in terms of probability of bit error and probability of packet error. The results presented in this section illustrate the potential of RB-HARQ combined with

28 Average number of bit indices fed back and Average number of information bits requested N F N R E s / N o (db) Figure 2.6: Average number of bit indices fedback ( ) and average number of information bits requested for retransmission ( ) vs. for RB-HARQ scheme. RCPC codes. For all of the results presented in this chapter, the information packet transmitted from to is encoded using a convolutional code of rate, constraint length with generator polynomials (in octal) and. In this chapter, we present the results for a block size of information bits, including the tail bits. The first transmission for every packet is at rate higher than. This is achieved by puncturing the rate code using the puncturing pattern specified in the work by Hagenauer [7]. If packet is received in error at, it sends a retransmission request to. In this work we consider the use of lossless arithmetic coding [28] to compress the retransmission-request packet. The source initially transmits the packet using either a rate or convolutional code. If fails to decode the packet correctly, it sends a retransmission-request packet containing a list of the positions of either or of the least-reliable information bits. The numbers and

29 No ARQ After 1st retransmission After 2nd retransmission After 3rd retransmission 10 2 Probability of bit error Effective E b / N o (db) Figure 2.7: Probability of bit error vs. Effective for RB-HARQ scheme with variable redundancy and reduced retransmission-request packet are chosen so that in the next section we can make a fair comparison between the proposed scheme and the HARQ scheme proposed by Hagenauer [7]. In studies that consider RB-HARQ based on turbo codes [21, 22], responds to the request packet by retransmitting the information bits. However, the code in these studies [21, 22] is a systematic turbo code, whereas the code we consider in this work is a nonsystematic convolutional code. Thus, for these results, retransmits the two code bits corresponding to each of the positions identified by. To further clarify, is using the reliability of the information bits to identify unreliable sections in the code trellis and then requests new code information for those trellis sections. The received code symbols are combined with all previously received

30 & & copies of those symbols. For BPSK transmission over an AWGN channel, the soft-outputs for the symbols can be added together. 18 For the results presented in this section, each packet consists of bits, including the tail bits. For initial transmission rate, a total of information ) ( coded bits per packet are transmitted in the first transmission. Each retransmission request consists of a list of bit positions, and transmits code bits in response to each request. This corresponds to incremental redundancy per retransmission. We consider the performance when the request and retransmission process can occur up to five times. Each retransmission effectively reduces the code rate. After five retransmissions, a total of ( & ) coded bits are received at. Thus the code rate after five retransmissions is. For initial transmission rate, a total of ( ) coded bits per packet are transmitted in the first transmission. Each retransmission request consists of a list of bit positions and transmits code bits in response to each request. After five retransmissions, a total of ( & ) coded bits are received at, thus lowering the code rate to. Note that in this section, the size of the retransmission-request packet is not taken into account; the additional overhead from the request packet is considered in Section 2.4.2, where we evaluate the throughput. The results in Figure 2.8 and Figure 2.9 show the probability of bit error and probability of packet error, respectively, as a function of the channel symbol energy-to-noise density ratio ( ). The initial code rate for these results is. In Figure 2.8 we observe that to achieve a probability of bit error of, a system using the proposed RB- HARQ technique with five retransmissions of incremental redundancy each requires db lower than a system that uses rate code with no ARQ. This is a significant performance gain, and most of it has been achieved after only two retransmissions. It should be noted that the error curves indicate flooring at higher values of. The results in Figure 2.9 show that to achieve a probability of packet error of, a system

31 19 using the proposed RB-HARQ technique with five retransmissions of incremental redundancy each requires db lower than a system that uses rate code with no ARQ. The results in Figure 2.10 and 2.11 show the probability of bit error and probability of packet error, respectively, for the initial code rate. In Figure 2.10 we observe that to achieve a probability of bit error of, a system using the proposed RB-HARQ technique with five retransmissions of incremental redundancy each requires db lower than a system that uses rate code with no ARQ. In Figure 2.11 we observe that to achieve a probability of packet error of, a system using the proposed RB-HARQ technique with five retransmissions of incremental redundancy each requires db lower than a system that uses rate code with no ARQ. These results show that the proposed technique can significantly improve the performance of communication systems where convolutional codes are used, provided there is a reliable feedback channel for retransmission-request packets Error Probability Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the proposed technique with the HARQ scheme proposed by Hagenauer [7] (RCPC-HARQ). We compare the two schemes in terms of probability of bit error and probability of packet error. Results in Figures 2.10 and 2.11 show the performance comparison of the two schemes when the initial code rate is. Every packet is first transmitted using a rate convolutional code. The RCPC-HARQ scheme, in response to a NACK, moves to a lower code rate by retransmitting bits in each retransmission thus achieving rate after two retransmissions. The performance of the RCPC-HARQ scheme is shown in Figures 2.10 and 2.11 using solid lines. In the RB-HARQ scheme, that we propose, bits are transmitted in a series of five retransmissions thus achieving a rate after five retransmissions. The performance of the RB-HARQ scheme is shown in Figures 2.10 and 2.11 using dashed lines. In Figure 2.10 we observe that to achieve a probability of bit error of, the proposed RB-HARQ scheme requires db lower than the RCPC-HARQ scheme. In

32 first transmission rate 4/7 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 1/2 Probability of bit error /2 4/7 1/ E s / N 0 (db) Figure 2.8: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 4/7. Figure 2.11 we observe that to achieve a probability of packet error of, the proposed RB-HARQ scheme requires db lower than the RCPC-HARQ scheme. Thus we conclude that the proposed scheme achieves significant performance improvement over the RCPC-HARQ scheme. Note that this gain is achieved at the cost of large retransmissionrequest packets and more retransmissions than in the RCPC-HARQ scheme Throughput Comparison of RB-HARQ with HARQ with RCPC codes In this section we compare the performance of the two schemes in terms of throughput. We do the performance comparison for the case when the initial code rate is. First let us consider the size of retransmission-request packet in the proposed scheme. As previously mentioned, the retransmission-request packet consists of the least reliable bit positions.

33 /7 Probability of packet error /2 1/ first transmission rate 4/7 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 1/ E s / N 0 (db) Figure 2.9: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 4/7. For a packet of information bits, each bit position can be represented by a index. Thus each retransmission-request packet consists of -bit bits if no source coding is used. However we can apply arithmetic coding to compress the retransmission-request packet. The way the compressed retransmission-request packet is generated is as follows. The destination radio constructs an all-zero bit packet of size equal to the number of information bits in the transmitted packet. Thus for the results presented in this paper, constructs a packet of bits. Then it places a one in the bit positions corresponding to the least reliable bit positions. Thus the packet consists of zeros and ones. The arithmetic coding is then applied on this bit packet that consists of zeros and ones. Our results show that arithmetic coding produces compressed retransmission-request

34 / /7 Probability of bit error / rate 2/3 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 4/7 rate 1/ E s / N 0 (db) 1/2 Figure 2.10: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 2/3. packets that have an average size of ( bits thus achieving a compression ratio of ). Thus by using arithmetic coding we are able to save every time a retransmission-request packet is sent from to. ( minus ) bits Figure 2.12 illustrates the throughput of the RCPC-HARQ scheme proposed by Hagenauer [7] and the RB-HARQ scheme proposed in this paper. We assume that when the limits of retransmission are reached for either HARQ scheme, the packet is retransmitted at the original rate and the HARQ process begins again. Then the throughput is defined as the ratio of the number of bits per packet to the expected number of coded bits that must be transmitted to achieve correct decoding of the packet. Thus, the throughput is given by

35 / /7 Probability of packet error / rate 2/3 first retransmission second retransmission third retransmission fourth retransmission fifth retransmission rate 4/7 rate 1/ E s / N 0 (db) 1/2 Figure 2.11: Performance comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate 2/3. where is the packet size in bits, is the expected number of coded bits that are transmitted in both the directions by the HARQ process, and is the probability of packet success by the end of the HARQ process. In our simulations, throughput is calculated as the ratio of number of information bits in packets that are decoded correctly to the total number of bits transmitted in both the directions. The throughput of the RCPC- HARQ scheme is illustrated by the curve labeled by RCPC-HARQ. The curves labeled RB-HARQ, and illustrate the performance of the proposed RB-HARQ schemes. For RB-HARQ2, the retransmission-request packet is sent without source coding. For RB- HARQ3, retransmission-request packet is sent with source encoding at. RB-HARQ4 denotes the throughput of the proposed RB-HARQ scheme without taking into account retransmission-request packet. Thus, RB-HARQ4 can be interpreted as the throughput

36 24 when the overhead on the retransmission request is not considered important, or RB- HARQ4 can be interpreted as a simple, loose upper bound on the throughput that can be achieved with any source coding algorithm. Results in Figure 2.12 show that the proposed scheme achieves significantly higher throughput at most signal to noise ratios. For example, at db the throughput (RCPC-HARQ) of the RCPC-HARQ scheme is approximately while the throughput of the proposed scheme with compressed retransmissionrequest packet (RB-HARQ3) is approximately. The results show that even if we send the retransmission-request packet without any source coding, we still achieve a higher throughput (RB-HARQ2) than the RCPC-HARQ scheme. 0.5 RCPC HARQ RB HARQ2 RB HARQ3 RB HARQ4 0.4 Throughput E / N s 0 (db) Figure 2.12: Throughput comparison of the proposed RB-HARQ scheme with the RCPC- HARQ scheme with initial code rate.

37 CHAPTER 3 RELIABILITY-BASED HYBRID ARQ FOR PARTIAL-TIME JAMMING CHANNELS In this chapter we extend the RB-HARQ technique to improve performance in a hostile jamming environment. Consider the communication scenario shown in Figure 3.1 in which the transmitter is communicating with the receiver in the presence of a partialtime jammer. We consider an asymmetric situation in which the receiver ( ) and the transmitter ( ) experience different levels of jamming. In particular, we focus on the scenario in which the receiver is experiencing high jamming levels compared to the transmitter. Figure 3.1: Communication scenario. The system model for the above communication scenario is shown in Figure 3.2. We consider packetized communication in which packets at are encoded using a convolutional code for transmission to. Code symbols are modulated using BPSK and received in the presence of white Gaussian thermal noise and time-varying jamming. The jammer is modeled using a discrete-time two-state Markov model as shown in Figure 3.3. If at time the jammer is in state, then the code symbol transmitted at time is not jammed. State indicates that the jammer is on and the code symbol is jammed. The proportion of time for which the jammer is active is specified as, and represents the expected value of the time (in terms of number of code symbols) spent in the jamming state before returning 25