Adaptive Scheduling for Multicasting Hard Deadline Constrained Prioritized Data via Network Coding

Transcription

1 Adaptive Scheduing for Muticting Hard Deadine Constrained Prioritized Data via Networ Coding Tuan T. Tran 1, Hongxiang Li 1,WeiyaoLin 2, Lingjia Liu 3, and Samee U. Khan 4 1 Department of Eectrica and Computer Engineering, J.B. Speed Schoo of Engineering, University of Louisvie, KY Institute of Image Communication and Information Processing, Shanghai Jiaotong University, China. 3 Department of Eectrica Engineering and Computer Science, The University of Kans, Lawrence, KS Department of Eectrica and Computer Engineering North Daota State University, Fargo, ND Emai: tttran14@ouisvie.edu Abstract Networ coding offers a promising patform for mutict transmission by approaching its min-cut capacity. However, pushing the networ throughput toward this upper bound comes with a sacrifice in deivery deay due to the decoding procedure that requires performing batch of coded pacets. Further, in some transmission scenarios where the receivers experience deep fading or unabe to coect a fu set of the transmitted data, no usefu information is recovered. The effect is more severe in the networs where the transmitted information h priority structure with hard deadine constraint due to the imited deivery time and data interdependencies. In this paper, we consider singe-hop wireess networs where the transmitter wishes to mutict hard deadine constrained prioritized data to many receivers over ossy channes. We first study the networ performance of a variety of transmission techniques, depending on how the transmitter schedues transmission in each time sot. We then propose an adaptive encoding and scheduing technique to maximize the networ throughput. To find the optima transmission scheduing at the presence of the networ dynamics, we ct the probem in the framewor of Marov Decision Processes (MDP) and use bacward induction method to find an optima soution. We further propose simuation-bed agorithm and greedy scheduing technique that obtain high performance with much ower time compexity. Both anaytica and simuation resuts have been provided to corroborate the effectiveness of the proposed techniques. Index Terms Mutict, hard deadine constraint, prioritized transmission, adaptive scheduing, networ coding. I. INTRODUCTION Mutimedia networing appications over wireess networs have gained much popuarity recenty. Unie other types of traffic, mutimedia traffic such video requires a higher eve of quaity of service (QoS), e.g., minimum bandwidth and maximum deay toerance, to meet user satisfactions. However, the current wireess networs such WiFi were not designed for efficient provisioning of networ resources in order to guarantee some specified QoS. To mitigate this ac of infrtructure support, scaabe compression techniques are used to aow the sender to dynamicay adjust the media bitrate to the current avaiabe bandwidth in rea time. Notaby, scaabe video coding (SVC) [14] is a cs of techniques that aows a sender to adapt its video bit rate by partitioning a video bit stream into a be ayer and severa enhancement ayers. The receiver is then abe to view the video with higher quaity when more ayers are received. The be ayer is the most important ayer and must be present in order to have a reonabe video quaity. The enhancement ayers are organized in a hierarchica fhion such that the first enhancement ayer must be present for the second enhancement ayer to be usefu, and the second enhancement ayer must be present for the third enhancement ayer to be usefu, and so on. Naturay, this scenario eads to the genera probem of prioritized transmissions where the goa is to transmit the most usefu data under some resource constraints. To deiver prioritized data to mutipe users in wireess networs, muticting is a we-suited emerging technoogy. The underying principe of wireess mutict is to expoit the inherent broadct nature of a wireess networ. That is, a transmitted pacet can be intercepted by mutipe receivers in the transmission range of the sender [6], [16]. As a resut, the required bandwidth and power consumption are substantiay reduced compared to the unict protocos. However, designing an efficient mutict protoco for prioritized transmissions is quite chaenging due to the ossy nature of wireess channes, and the heterogeneity in the amount of information correcty received across different receivers. In addition, it needs to tace the bottenec effectofthe shared transmission medium among many receivers, i.e., the overa performance is imited by the receiver that h the worst channe condition. With that said, ensuring the QoS for the bottenec user on par with the others ceary maes the mutict transmission more chaenging. Fortunatey, networ coding (NC), a recent routing protoco proposed by Ahswede et a. [1], offers a promising patform for mutict transmissions. Indeed, it h been proved that one can approach the mutict capacity by using random inear networ coding technique [10], by which the intermediate nodes form output data by ineary combining the input data. A receiver is abe to decode the origina transmitted data when it receives a fu set of independent coded pacets. This method is simpe, efficient, and decentraized in the sense that the coded pacets are independenty generated at intermediate nodes. However, random networ coding may come with a sacrifice in deivery deay due to the decoding procedure that requires performing batch of coded pacets. In addition, receivers need to coect a fu set of the coded pacets in order to recover the transmitted data, e.g., by Gaussian eimination. Speciay, when ony partia set of the coded pacets is received, no usefu information is recovered. As a resut, it substantiay decrees the QoS of receivers that are unabe to coect enough data during the transmission period. The effect is more severe in transmission scenarios where the transmitted information h priority structure with hard deadine constraint due to the imited deivery time and data interdependencies. Without any carefu encoding and scheduing design, the effect can be detrimenta. Therefore, in this paper, we investigate transmission scheduing strategies in wireess networs where the transmitter wishes to mutict hard deadine constrained prioritized data to many receivers over ossy channes. This framewor

2 can be used to mode many practica networs such mutimedia streaming in the t-mie networs, or remotey reprogramming the sensors in unreachabe fieds. In our mode, we aow the transmitter to use random networ coding (RNC) [10] to encode the incoming data pacets before sending them out. The t of the transmitter is to schedue pacet transmissions, i.e., seecting which pacets in which time sots, in order to maximize the networ throughput. Particuary, we propose an adaptive encoding and scheduing technique bed on the framewor of Marov Decision Processes (MDP) to expoit the feedbac information from the receivers. Further, to reduce the time compexity of the standard agorithm that finds the optima soution to the MDP, we propose simuationbed agorithm and greedy scheduing technique. Our main contributions in this paper are foows. We study in detai a variety of transmission techniques, depending on different transmission scheduing strategies. We then design an adaptive encoding and scheduing technique that maximizes the networ throughput bed on the framewor of MDP. We further propose simuation-bed agorithm and greedy scheduing technique that approximate an optima networ performance with much ower time compexity. We corroborate the effectiveness of the proposed techniques through both theoretica anaysis and simuations. The organization of the paper is foows. We provide in Section II some preiminaries and reated wor. In Section III, we describe the system mode and probem formuation. In Section IV, we study in detai a variety of transmission techniques and anayze the corresponding networ performance. Simuation resuts and discussions are provided in Section V. Finay, we concude the paper in Section VI. II. PRELIMINARIES AND RELATED WORK Formay, the prioritized data refers to the notion that, given L prioritized pacets in the decreing order of importance, a 1 a 2 a L, to be deivered to a receiver, then the pacet a i is usefu to the receiver ony if it h received a its interdependent pacets a j with j < i successfuy. Those interdependencies are graphicay represented in Fig. 1(a), in which a 1 is the most important data pacet and it needs to be decoded first in order to the other pacets to be decoded. Simiary, Fig. 1(b) represents the dependencies of video frames of a group of pictures (GOP) often used in MPEG standard [7]. As shown, frame B 1 can be decoded ony if its dependent frames I and P 1 aso have been decoded. Aso, frame P 1 can be decoded ony if frame I h been decoded. Eventuay, represented in the graph, data pacet containing frame I is the most important data pacet that needs to be decoded first in order to decode the GOP. That said, when deaing with the prioritized data, receiving more data pacets may not necessariy resut in higher QoS. This is because received data pacets which are missing their interdependencies cannot be decoded. Thus, to compare the performance between two prioritized transmission techniques, we use the effective throughput, i.e., the data that contributes to the improvement of the QoS at receivers. In the iterature, muticting hard deadine constrained data h been studied in [2], [3]. In these wors, the authors considered one-hop wireess networs with random incoming data and proposed scheduing strategies to minimize the system energy. These wors focused on deriving energy bounds from theoretica view point and did not consider prioritized data. On the other hand, in the context of streaming of prioritized data over ossy wired networ, Chou et a. [5] proposed a heuristic agorithm to minimize the rate-distortion of the stream. In another wor, Tran et a. [15] proposed a cs of approximate Fig. 1. Exampes of data interdependence graphs. (a) Sequentia dependencies of prioritized data. (b) Dependencies of video frames of a group of pictures (GOP) using MPEG standard. agorithms bed on the framewor of Marov Chain Monte Caro (MCMC) to maximize the sum throughput of a wireess broadct networ. However, in this wor the authors sumed that the transmitter is an orace which nows the channe conditions of a time sots in advance. Aong in a different avenue, since the pioneering wor of Ahwede [1], NC h received much attention. In particuar, in the context of noiseess mutipe-source mutict transmission over wired networs, Wu et a. [17] proposed a practica communication scheme for a ce with two sources. The proposed scheme achieved ow compexity and robustness to the networ dynamics, but it resuted in a suboptima performance. In another wor, Goe et a. [9] derived a ower bound of energy consumed in wireess mutict networs using NC. Further, some adaptive NC schemes have been proposed in wireess networs to incree the networ throughput and bandwidth efficiency [11], [12], [13]. However, a these wors did not consider prioritized data or focused ony on heuristic agorithms to minimize the decoding deay of specia scenarios with imited number of receivers. Different from these wors, we investigate a genera framewor by empoying adaptive networ coding for muticting prioritized data with hard deadine constraint over error-prone channes. III. SYSTEM MODEL Consider a singe hop wireess networ, such WiFi or WiMAX networs, where the transmitter wishes to mutict hard deadine constrained prioritized data to many receivers. We sume that system operates on a singe frequency and the communication channes between the transmitter and receivers are ossy, i.e., each pacet transmitted to receiver R is subject to an erure probabiity ɛ. The erure probabiities are sumed to be independent and identicay distributed (i.i.d.) across receivers and time. We sume that the system is timesotted and each sot ength corresponds to one pacet transmission. At the transmitter, random incoming data pacets are accumuated in its buffer before encoding and sending them out. Optima accumuation strategy is not the focus of this paper. Instead, in this paper we are particuary interested in designing adaptive encoding and scheduing schemes to maximize the networ throughput. We sume that the transmitter h L prioritized data pacets in the order of importance: a 1 a 2 a L, where their sequentia interdependencies are represented in Fig. 1(a). The transmitter wants to transmit these data pacets to K receivers over erure channes within a deadine T L time sots. Further, we sume that the receivers wi inform the transmitter whether a pacet h been received successfuy or not via one-bit feedbac messages. For the sae of carity, we sume that the feedbac messages are instantaneous and reiabe. However, the main principe of the framewor sti hods for the ce of unreiabe feedbac, and one can deveop a more accurate mode, abeit compicate

3 anaysis. At the receivers, a pacet a j is decoded ony if it is received before the deadine, and a of its interdependent pacets a i, i <j, aso have been received successfuy. We sume that the transmitter is abe to impement RNC over a arge finite fied F q. Different pacet encoding and scheduing schemes may resut in different networ throughputs. In order to achieve the maximum networ throughput, the transmitter needs to carefuy encode and schedue data pacet in every time sot. Therefore, the main focus of this paper is to design adaptive encoding and scheduing techniques to maximize the networ throughput of muticting hard deadine constrained prioritized data over erure channes. Before deving into detais of the probem, we first provide a metric that wi be used throughout the paper the performance meure to compare different techniques. Definition 3.1: Assume the transmitter h L prioritized data pacets in the decreing order of importance a 1 a 2 a L sociated with a deadine of T time sots. Receiver R achieves a throughput η = m L pacets if it can recover m consecutive origina data pacets {a 1,a 2,...,a m } by the deadine T. The average networ throughput per time unit across K receivers is defined 1 K =1 η im η, (1) ζ ζ KT ζ where ζ is the operating time of the networ. Using this definition, a transmission technique A is better than technique B if η A >η B. IV. TRANSMISSION TECHNIQUES: PERFORMANCE ANALYSIS In this section, we wi investigate in detai a variety of transmission techniques for muticting hard deadine constrained prioritized data to mutipe receivers, depending on how the transmitter schedues transmission in each time sot. In particuar, we consider five transmission strategies: Automatic repeat-request, round-robin scheduing, random networ coding, and the new adaptive random networ coding and greedy scheduing techniques. For a techniques, we sume the transmitter h L prioritized data pacets which need to be deivered to K receivers within a hard deadine of T time sots. A. Automatic Repeat ReQuest (ARQ) This is a bic approach to deiver data to the receivers over error-prone channes. In this transmission protoco, after sending out a data pacet, the transmitter waits for feedbac messages, i.e., acnowedgements (ACKs) or negative acnowedgements (NAKs), from the receivers to decide which pacet wi be transmitted in the next time sot. If there exists at et a pacet oss at the receivers, the transmitter resends the ost pacet unti a receivers receive it correcty. We note that it does not necessariy require a receivers successfuy receive the transmitted data pacet in the same time sot the correcty received pacet can be stored in the receivers buffer. Intuitivey, the networ throughput of the data muticting using ARQ technique is determined by the bottenec receiver, i.e, the receiver h the worst channe condition. With this observation, we wi use the toos of the order statistics to characterize the networ performance. Let X be the random variabe denoting the number of transmissions that the transmitter needs to attempt to deiver a pacet to receiver R. Further, define Y the number of transmissions required to deiver a pacet to a receivers, we then can write Y =max {1,...,K} {X }. The probabiity that the transmitter needs at most n transmissions to deiver a pacet to a receivers is given by ( ) P(Y n) =P max {X } n {1,...,K} (a) = K (1 ɛ n ), (2) =1 where (a) foows the resut of the geometric distribution with success probabiity 1 ɛ. Simiary, we have the probabiity that the transmitter needs ess than n transmissions to deiver a pacet to a receivers is given by P(Y < n)= K =1 1 ɛ n 1. (3) From (2) and (3), the expected number of transmissions needed to deiver a pacet to a receivers can be written E[Y ]= np(y = n) n=1 = 1 ( 1)i1+i2+ +ik i 1,i 2,...,i K 1 ɛ i1 1 ɛi2 2...ɛiK K, (4) where i 1,i 2,...,i K {0, 1}, i j 0. Therefore, after a ong operation, the average networ throughput per time sot across K receivers of the ARQ technique is written η = 1 E[Y ]. (5) B. Round-robin Scheduing (RRS) This is a bic time-sharing scheme where the transmitter sends the data pacets in a circuar order. Particuary, using this technique pacet a i is transmitted in time sots ts j if T j (mod L). Consider Exampe 1, for instance, we have L =3and T =4; thus pacet a 1 (i =1) wi be transmitted in time sots ts j where j = {1, 4} because T j (mod L). Let T i denote the number of time sots used for transmitting data pacet a i.wehavethat { T T i = L +1 if i T L T L ; T L otherwise, (6) where x denotes the argest integer not greater than x. The probabiity that pacet a i is received successfuy at receiver R is given by T i Ti P (a i )= ɛ Ti j (1 ɛ ) j. (7) j j=1 Let X i be the random variabe representing the event pacet a i can be decoded at receiver R after T time sots (this impies that a of its interdependent pacets are aso received successfuy.) Then, we have the probabiity that pacet a i is decoded at receiver R is i P (X i )= P (a j ) = j=1 i T j j=1 m=1 Tj ɛ Tj m (1 ɛ ) m. (8) m

4 Next, we obtain the expected throughput achieved at receiver R L η = P (X ). (9) =1 From (1), (8), (9), and considering the independent received data at each receiver, we obtain the average networ throughput η = 1 KT K L =1 =1 T j j=1 m=1 Tj ɛ Tj m (1 ɛ ) m, (10) m where T j is determined from (6). C. Random Networ Coding (RNC) In this transmission technique, the transmitter uses RNC to generate coded pacets and sends them out at every time sot. Particuary, a coded pacet is generated c i = L j=1 α ija j, where α ij are withdrawn randomy from the finite fied F q. Let X be the random variabe denoting the number of coded pacets received successfuy at receiver R. The probabiity that receiver R can recover a L origina data pacets is given by 1 T T P (X L) = (1 ɛ ) ɛ T. (11) =L We shoud note that once a receiver coects at et L coded pacets, it is abe to recover a the origina data pacets by soving the system of inear equations formed by the received coded pacets. Thus, the expected throughput achieved at receiver R is η = LP (X L) T T = L (1 ɛ ) ɛ T. (12) =L Simiary in ARQ technique, from (1), (11), (12), and considering the independent data received at the receivers, the average networ throughput of RNC technique is represented η = L KT K T =1 =L T (1 ɛ ) ɛ T. (13) D. Adaptive Random Networ Coding (ARNC) In this transmission technique, the transmitter expoits the feedbac information from the receivers to adaptivey encode and schedue coded pacet at every time sot to maximize the average networ throughput. We sume that at the beginning of each time sot the transmitter receives one-bit feedbac from the receivers to indicate whether the previous transmitted pacet h been received successfuy. Bed on that, the transmitter updates the networ state, i.e., which receiver h which pacets, and decides which pacet wi be sent out in the next time sot. Fortunatey, in this scenario the networ dynamics can be modeed a Marov Decision Process (MDP) in which the transmitter acts a decision maer to decide which action to tae from an action set at every time sot. We specify the networ dynamics by a six-tupe (S, A, P, r,t,γ), where we use bodface etters to refer to vectors or matrices. 1 Assume the finite fied F q is arge so that a coded pacets are independent. 1) State space S: A networ state s is defined by a matrix n 11 n n 1L s = n 21 n n 2L......, (14) n K1 n K2... n KL where an eement n ij represents the number of coded pacet, which is generated from a data batch of j origina pacets {a 1,a 2,...,a j } and received by receiver R i. 2) The action set A consists of actions sending coded pacets that are generated from different data generations (batches). In particuar, there have L generations where generation G i consists of i consecutive origina pacets {a 1,a 2,...,a i }. We then denote a coded pacet which is generated from data generation G i c i. 3) The transition distribution P(s t+1 s t,a t ) is computed bed on the networ current state, s t, action taen, a t, and pacet erure probabiity of the channe to each receiver. For exampe, in the ce of two receivers [ and ] L =2. If the networ current state is s t =, and the transmitter taes action a t = sending a coded pacet c 1 G 1, [ the probabiity ] that the networ transits 1 0 to state s t+1 = is P (s t+1 s t,a t )=(1 ɛ 1 )ɛ 2. This scenario occurs when R 1 and R 2 correspondingy succeeds and fais to receive the transmitted pacet. 4) The immediate reward matrix r(s, a) is computed bed on the future-dependent reward function r(s t+1 s t,a t ) r(s t,a t )= r(s t+1 s t,a t )P (s t+1 s t,a t ). (15) s t+1 S If we define the termina reward r(s T ) η st, i.e., the average networ throughput when the networ is in state s T, we then eventuay can compute the immediate rewards of a intermediate states. This reward function is designed to refect whether the receivers are abe to decode the transmitted data. Its principe is simiar to a deay reward signment, i.e., the intermediate states, in which the receiver does not have enough data to recover the transmitted data, shoud have a zero immediate reward. 5) T is the number of stages or time sots sociated with the current data batch. 6) γ [0, 1) is discount factor. When γ is cose to zero, the transmitter tends to consider ony immediate reward, and γ is cose to one, the transmitter prefers future reward with higher weight. The vaue of γ is adjusted to baance between exporation and expoitation. A transmission poicy is defined a strategy bed on which the transmitter chooses an action corresponding to each state and time sot. Let a non-negative rea vaue function V π : S R represent the expected reward obtained by foowing poicy π at each state in S. Assume that at the beginning the system is in state s, the expected tota reward using any such poicy π is defined V π (s) =E [ T 1 t=0 ] γ t r(s t,π(s t )) + γ T r(s T ) s 0 = s, (16) where E[.] is the expected function. The cumuative reward from time step t to T is recursivey computed using bacward induction foows

5 V π (s t )=r(s t,π(s t )) + E [γv π (s t+1 )] = r (s t,π(s t )) + γ P (s t+1 s t,π(s t ))V π (s t+1 ), s t+1 S (17) where t = {T 1,...,0}. We are seeing for an optima poicy π in T steps that maximizes the expected cumuative reward. We have that π =argmax {V π(s t )} (18) π To find an optima poicy, we can use the bacward induction agorithm (BIA). The main principe of this agorithm is that it initiaizes immediate rewards for a termina states then computes the expected rewards of the intermediate states bacwardy. Specificay, in the time-horizon the agorithm runs from T 1 to zero, and in each iteration it computes the immediate reward for each pair of state and action bed on the immediate rewards of the future states. The time compexity of the BIA is O(T S 2 A ) and it is subject to the curse of dimensionaity when deaing with a arge space probem. To tace this probem, we use the simuation-bed method [4] to approximate the optima poicy. In particuar, our agorithm combines bacward induction with simuation-bed methods to reduce the time compexity to O(TΔ S A ) with Δ S. The pseudocode of the simuation-bed bacward induction agorithm (SBIA) is summarized in Agorithm 1. Agorithm 1 : Simuation-bed Bacward Induction Agorithm (SBIA) Input: S, A, P, r,t,γ,δ. Output: π = {d(s 1 ),d(s 2 ),...,d(s T )} 1: Initiaize: t = T,setV (s T ):=0and r(s T ):=η st for s T S 2: for t := T 1 to 0 do 3: for each state s t S do 4: try a actions a t A st for Δ iterations, and compute 5: V (s t,a t )= 1 Δ Δ [r(s t+1 s t,a t )P (s t+1 s t,a t ) 6: +γv (s t+1 )] } 7: V (s t )=max at A { V (s t,a t ) { } 8: d(s t ) = arg max at A V (s t,a t ) 9: end for 10: end for Remar 1: At the beginning, the networ state is initiaized s 0 =[0], i.e., matrix with a eements are zero. Remar 2: So far, we have soved the probem with reiabe feedbac messages. In practice, however, feedbac messages are subject to osses and errors; thus, the transmitter observes ony partia of the networ states. Fortunatey, this ce can be formuated a Hidden Marov Mode (HMM) and soved by the same SBIA agorithm with V (o t,a t )= 1 [r(o t+1 o t,a t )P (o t+1 o t,a t )+γv (o t+1 )], Δ Δ (19) where o t is the observed state at time step t. E. Greedy Scheduing Technique (GST) Intuitivey, the GST is of interest because it woud have much ess time compexity compared to the SBIA agorithm. In this technique, the transmitter sees for an action that maximizes the networ throughput considering ony one time step ahead. In particuar, bed on the feedbac information from the receivers, the transmitter updates the networ state and seects a coded pacet to transmit in the next time sot to maximize the one time step future-reward. The GST technique may not resut in a goba optima soution after T steps, but it may yied ocay optima soution that approximates the goba optima soution. To get a concrete sense, consider the exampe [ in Section ] IV-D with the current state of the networ s t =. Using GST technique, an optima action in the next time sot is to send pacet c 1 G 1. This is because no pacet h been received, and c 1 is the most important pacet that a receivers need to have to be abe to decode other pacets. Specificay, the optima action a t taen at time step t to maximize one time step future-reward is expressed a t =argmax P (s t+1 s t,a t )r(s t+1 ). (20) a t A We can see that the time compexity of the GST agorithm is O(T A ). It is much ess than that of the BIA and SBIA agorithms, and more importanty, it does not depend on the size of the state space and a actions are computed on the fy. Average networ throughput (pt/sot) Number of receivers ARNC RNC ARQ RRS GST Fig. 2. Networ throughput vs. number of receivers. V. SIMULATION RESULTS AND DISCUSSIONS In this section, we iustrate the performance gain of the proposed techniques via simuations. We start with the bic setup. A. Bic Setup In our simuation, we sume that each data batch consists of a mutimedia frame, e.g., Aiyo [8], prioritized into four interdependent ayers in the decreing order of importance a 1 a 2 a 3 a 4, where each ayer is sumed can be encapsuated into one pacet. To reduce the size of the state space, we categorize the prioritized data into two generations G 2 = {a 1,a 2 } and G 4 = {a 1,a 2,a 3,a 4 }. Further, we sume that the erure channes between the transmitter and receivers are independent. The average networ throughput is determined the mean of the average networ throughputs across a receivers defined in Eq. (1) over 10, 000 trias. B. Simuation Resuts First, we investigate the impact of networ size on the networ throughput of different techniques in Fig. 2. In this experiment, we fix the deadine T =8time sots and vary the number of receivers. To simuate the heterogeneity of channes, we sume that the pacet erure probabiities of the transmission channes are different and set 10%, 12%, 15%, 17%, and

6 Average networ throughput (pt/sot) Fig. 3. ARNC RNC ARQ RRS GST Pacet erure probabiity Networ throughput vs. pacet erure probabiity. 20% (corresponding to ɛ 1,...,ɛ 5 ). As expected, the average networ throughput of each technique decrees with the incree of number of receivers. This is because of the higher erure probabiities of the new added receivers and the heterogeneity in the amount of information received across the receivers. Further, we observe that with the higher number of receivers, i.e., K =5, ARQ technique suffers the bottenec effect in which retransmissions dupicate received data at receivers with good channe conditions; consequentiay, the networ throughput decrees significanty. It is cear that ARNC technique achieves the best performance by empoying an adaptive encoding and scheduing transmissions over T time sots, and its performance gain increes substantiay in the ces of arger number of receivers. This is because each transmitted pacet using ARNC technique brings innovative information to many receivers, everaging the bottenec effect. On the other hand, GST technique using one-time-step ahead scheduing significanty reduces the time-compexity whie sti obtaining a performance very cose to that of ARNC. Next, Fig. 3 depicts the average networ throughput of different techniques with respect to the pacet erure probabiities. In this experiment, we fix the number of receivers K =5and vary the erure probabiities of the transmission channes. Specificay, we sume that a channes have the same erure probabiity ɛ, and we vary ɛ from 5% to 20% with step size of 3%. AsseeninFig.3,whentheerure probabiity ɛ is sma, a the techniques obtain high networ throughput and the performance gains among the techniques are sma. Our intuition is that when the erure probabiities are sma, each transmitted pacet is received successfuy at the receivers with high probabiity. Consequenty, most of the transmitted data can be decoded at the receivers. On the other hand, in the high-erure regime. i.e., ɛ = 20%, the networ throughput decrees substantiay. This is because there are more pacet osses due higher erure probabiities. Further, we observe that the performance gains among the techniques enarge significanty. In particuar, the ARQ technique, that the transmitter may need to retransmit a ost pacet many times woud dupicate received data at receivers, resut in the worst performance. On the other hand, expected, ARNC technique obtains the best performance whie GST approximates that of ARNC with much ower time compexity. techniques, depending on how the transmitter schedues transmission in each time sot. We further designed an adaptive encoding and scheduing technique bed on the framewor of MDP to maximize the networ throughput. The bacward induction agorithm (BIA) w used to find an optima transmission strategy. To reduce the time compexity of the standard BIA agorithm, we proposed sampe-bed bacward induction agorithm and greedy scheduing technique that have much ower time compexity, but sti achieving high performance. Both anaytica and simuation resuts have been provided to support the effectiveness of the proposed techniques. ACKNOWLEDGMENT This wor is partiay supported by the US Nationa Science Foundation (Grant No ), Kentucy NASA EPSCoR (Grant No ), Nationa Natura Science Foundation of China (Grant No ), and the Open Project Program of the Chinese Nationa Laboratory of Pattern Recognition (NLPR). REFERENCES [1] R. Ahswede, N. Cai, R. Li, and R. W. Yeung. Networ information fow. IEEE Transactions on Information Theory, 46: , Juy [2] M.M. Butt, K. Kansanen, and R.R. Muer. Hard deadine constrained mutiuser scheduing for random arrivas. In Wireess Communications and Networing Conference (WCNC), 2011 IEEE, pages , [3] M.M. Butt, K. Kansanen, and R.R. Muer. 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