MULTIPLEXING SCHEMES AND ARQ PROTOCOLS FOR MULTIPLE-RECEIVER SYSTEMS. Richard Cam. BASc (Engineering Physics), University of British Columbia, 1986

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1 MULTIPLEXING SCHEMES AND ARQ PROTOCOLS FOR MULTIPLE-RECEIVER SYSTEMS by Richard Cam BASc (Engineering Physics), University of British Columbia, 1986 MASc (Physics), University of British Columbia, 1989 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October 1994 Richard Cam, 1994

2 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. (Signature) Department of Electrical Engineering The University of British Columbia Vancouver, Canada Date 14 October 1994 DE-6 (2/88)

3 Abstract The throughput performances of some multiplexing and ARQ schemes are evaluated for a multiple-receiver system in which the quality of the channels varies over time. Packetized data are sent to the receivers from a server (transmitter), which uses a multiplexing scheme to assign bandwidth, as well as an ARQ protocol for error control. Two multiplexing schemes, roundrobin multiplexing and an adaptive scheme, are considered. In round-robin multiplexing, each receiver is served periodically. With the adaptive scheme, the transmitter selects at each slot, the receiver whose channel quality is judged to have the highest probability of successful data packet reception. These multiplexing schemes are evaluated in conjunction with the three standard ARQ schemes, stop-and-wait, go-back-n, and ideal selective repeat ARQ. The throughput analysis takes into account the effects of feedback errors and imperfect channel state estimates. A scheme for reducing the unfavorable effects of feedback errors on the performance of continuous ARQ protocols is proposed and analyzed for a point-to-point stationary channel. In this scheme, the transmitter may not immediately retransmit a packet that has timed out but whose status is unknown due to lost feedback. Instead, the transmitter may delay retransmission for up to a given number of slots (the retransmission delay parameter ), sending new packets in the mean time while waiting for successfully received feedback. The analysis considers the case where complete information of the receiver state is fed back to the transmitter. Under this assumption, it is shown that the effects of feedback errors can be greatly reduced when the retransmission delay parameter is optimized. This scheme is extended to the multiple-receiver system as well. Also discussed is a procedure for maximizing the effective data transmission rate of an ARQ system under certain bandwidth and power constraints. The procedure provides a means for jointly optimizing system design parameters such as the packet length, as well as coding and modulation schemes. The principles behind this procedure may also be useful for evaluating and optimizing the data transmission rate performance of the multiple-receiver system. II

4 Table of Contents Abstract List of Tables List of Figures Glossary Acknowledgment ii vii viii xi xiv 1 Introduction Preliminaries Reliable Data Communication FEC and ARQ Point-to-Multipoint ARQ J.4 Multiplexing and Multicast Systems A Brief Summary of Related Work Analysis Systems Multi-copy Transmission Type-I HARQ Type-lI HARQ Code Combining Optimum Packet Length Point-to-multipoint ARQ ,3 Summary of Contributions. 13 Ill

5 2 Some Aspects of ARQ Throughput Performance in the Presence of Feedback Errors Introduction A Buffer-Constrained Model for ARQ Protocols The Feedback Chamiel ,,,,,,..., A Postponed Retransmission Variation for Continuous ARQ Protocols Throughput Analysis Numerical Results Summary and Concluding Remarks 47 3 A Unified Approach to Data Transmission Rate Analysis for ARQ Systems Introduction System Model Data Transmission Rate Analysis Preliminary Calculations Synchronization Issues and Modulation Schemes Packet Error Probabifity with Convolutional Coding Packet Error Probabifity with Reed-Solomon Codes ARQ and Data Transmission Rate Numerical Results Concluding Remarks 64 4 Multiplexed ARQ: Throughput Analysis, Part I Introduction System Model Throughput Calculation Round-Robin Multiplexing ISRARQ ,1.2 GBNARQ 72 iv

6 SWARQ Adaptive Multiplexing 79 4,3,2,1 TSR ARQ GBN ARQ SW ARQ 84 5 Multiplexed ARQ: Throughput Analysis, Part II 86 5,1 Introduction Extension of Throughput Analysis Round-Robin Multiplexing Adaptive Multiplexing Reduced State Space Analysis Round-Robin Multiplexing m = m = 2...,...,.,., m = 3,.,...,...,,.,,,..,,., m = 4: Adaptive Multiplexing m = m = m = m = Multiplexed ARQ: Numerical Results Introduction Throughput Performance Comparisons Concluding Remarks V

7 7 Concluding Remarks 116 A Conditions for Continuous-Mode Half-Duplex Transmission over a Direct Link 118 A.1 Introduction 118 A.2 Analysis. 118 B Packet Synchronization Analysis 120 B.l Model 120 B,2 Analysis 121 B,3 Numerical Results 122 B.4 Concludthg Remarks 122 C Representation and Analysis of the Complete Multiple-Channel State Space 124 C.1 Size of State Space 124 C.2 Indexing the States 126 C.3 State Transition, State Estimation Error, and Selection Probabifity Calculations. 127 D Derivation of the g Function 129 E Analysis of an Equivalent Reduced Semi-Markov Process 130 E.1 Introduction 130 E.2 Analysis 131 E.2. 1 Transition Probabifities 131 E.2.2 Average Number of Successes 131 E.2.3 Average Number of Times Selected 133 E.3 Concluding Remarks 134 Bibliography 135 vi

8 List of Tables 2.1 Throughput of SW ARQ, N = 10,, Optimal values of w for GBN ARQ, N = 10. Optimal values of w for GBN ARQ, N = 100 Comparison between calculated throughputs for GBN ARQ from Eqn. (2.2) and from Eqns. (21)-(27) of, N = Comparison between calculated throughputs for GBN ARQ from Eqn. (2.2) and from Eqns. (21)-(27) of, N = TSR-limit values of w for SR ARQ, N = ISR-limit values of w for SR ARQ, N = TSR-limit values of q for SR ARQ, N = ISR-limit values of q for SR ARQ, N = Stage mapping for round-robin multiplexing Stage mapping for adaptive multiplexing Retransmission and resequencing buffer sizes used in simulations for ISRARQ Optimal and quasi-optimal values of w for GBN ARQ in Channel Optimal and quasi-optimal values of w for GBN ARQ in Channel 2..,..., Optimal and quasi-optimal values of w for GBN ARQ in Channel vii

9 1 List of Figures 1.1 Block diagram of an ARQsystem Channel delay, N Point-to-multipoint system General multicast system Buffer capacities required for some ARQ protocols Samples of protocol operation for the PR scheme (N = 4, w = 2) Samples of packets lost when an FOP is received in error Redundant packet counted among N packets lost due to buffer overflow (N = 3, Throughput performance of GBN ARQ for N = 10, FF, Throughput performance. of GBN ARQ for N = 10, Pp, 1 = Throughput performance of GBN ARQ for N = 10, PF,1 = Throughput performance of GBN ARQ for N = 10, FF1 = Throughput performance of GBN ARQ for N = 10, FF2 = 0.0,0,3, and Throughput curves for GBN ARQ, N = 100, FF1 = Throughput curves for GBN ARQ, N = 100, PF,2 = 0.0,0.3, and Throughput curves for SR ARQ, N = 10, FF1 = Throughput curves for SR ARQ, N = 10, PF,i 2.14 Throughput curves for SR ARQ, N = 10, PF,1 = = Throughput curves for SR ARQ, N = 10, PF 1 = Throughput curves for SR ARQ, N = 10, PF, 2 = 0.0,0.1,0.2, and Plot of highest values of o as a function of W1 for FDP with GBN ARQ and convolutional coding Plot of highest values of c as a function of W1 for FDP with GBN ARQ and RS coding. 61 vu

10 3.3 Plot of highest values of a as a function of D1 for TDP with GBN ARQ and convolutional Plot of highest values of a as a function of D1 for TDP with GBN ARQ and RS coding Block diagram of multiplexing system Markov chain for four channel states State diagram of semi-markov process for round-robin multiplexing with go-back-n ARQ Timing diagram for -r 2 in the semi-markov process for round-robin multiplexing with go-back-n ARQ State diagram of semi-markov process for round robin multiplexing with stop and wait ARQ State diagram of semi-markov process for adaptive multiplexing with go-back-n ARQ State diagram of semi-markov process for adaptive multiplexing with stop and wait ARQ State diagram of the semi-markov process for round-robin multiplexing with GBN ARQandw> State diagram of the semi-markov process for adaptive multiplexing and GBN ARQ withw> State diagram of reduced state space representation Throughput performance of ISR ARQ under round-robin and adaptive multiplexing Throughput performance of GBN ARQ with w = 0, for Channel 1, under round-robin and adaptive multiplexing Throughput performance of GBN ARQ with w = 0, for Channel 2, under round-robin and adaptive multiplexing Throughput performance of GBN ARQ with w = 0, for Channel 3, under round-robin and adaptive multiplexing Throughput performance of GBN ARQ using quasi-optimal w, for Channel 1, under round-robin and adaptive multiplexing 111 ix

11 6.6 Throughput performance of GBN ARQ using quasi-optimal w, for Channel 2, under round-robin and adaptive multiplexing Throughput performance of GBN ARQ using quasi-optimal w, for Channel 3, under round-robin and adaptive multiplexing Throughput performance of SW ARQ under round-robin and adaptive 114 B.1 Probabifity of successful packet sync as a function of h for various channel SNRs 123 C,l (C.2) evaluated for different values of K and J 125 E.1 Original semi-markov process 132 E.2 Equivalent semi-markov process with reduced number of states 133 x

12 Glossary ABBREVIATIONS Some abbreviations used in the thesis are: A ACK ARQ BCH FAX FDP FEC FOP FSK GBN HARQ HDLC HF ISR MCD MACK PR PSK QPSK RR RS SNR SR TDMA TDP Adaptive Acknowledgment Automatic Repeat Request Bose, Chaudhuri, Hocquenghem (code) Facsimile Frequency Domain Partitioning Forward Error Correction First Outstanding Packet Frequency Shift Keying Go-Back-N Hybrid ARQ High-level Data Link Control High Frequency Ideal Selective Repeat Multiple Copy Decoding Negative Acknowledgment Postponed Retransmission Phase Shift Keying Quaternary Phase Shift Keying Round Robin Reed-Solomon (code) Signal to Noise Ratio Selective Repeat Time Division Multiple Access Time Domain Partitioning SYMBOLS The common symbols used in this thesis are defined below. a Information data transmission rate. xi

13 Average number of packet transmissions per successfully transmitted packet. 7 Ratio of energy per symbol to noise power spectral density. yij Probability that the channel is actually in state j, given that it is estimated to be in state i, 7 Effective received signal-to-noise power ratio. 6jj Kronecker delta function. Probability that the channel is estimated to be in state i, given that it is actually in state j. State of marked channel when complete channel state is c. Throughput efficiency of ARQ protocol. Probability that the receiver s observation of the joint state N slots ago is estimated to be i, given that it is actually j. Probabifity of finding the channel in state j. Probabifity that the channel is estimated to be in state j. Tm, Tb Time spent in mode m; time spent in given state if the next state entered is b., 2 Bit packing efficiency, in bits per second per Hz, of modulation scheme used over forward, feedback channel. Event that the channel is selected. Wi, B1 B2 Bit transmission rate over forward, feedback channel Size of retransmission buffer. In Chapter 3, length of blank time on forward channel. Size of resequencing buffer. In Chapter 3, length of blank time on feedback channel. D1, D2 Length of packet data field on forward, feedback channel. Probabifity that the transmitted packet is in joint channel state i, given that the channel N slots ago is estimated to have been in joint state j. Ji, J2 K Number channel states in forward, feedback channel. Number of channels. L1, L2 Total packet length on forward, feedback channel. xii

14 N Round-trip delay, measured in packets, from the start of packet transmission to when the corresponding acknowledgment is expected. Bit error probability. FE FF,1, FF,2 pci) pci) p1(i) F Pj (N) i3 p(c) R Psync q S Qij Symbol error probability. Post-decoding packet error probability over forward, feedback channel. Post-decoding packet error probability over forward, feedback channel, given that the channel is in state j. Probability that the transmitted packet is received in error and is not redundant, given that it is in channel state j. Channel state transition probability. N-step channel state transition probability. Probability that the transmitted packet is redundant given that the channel is in state c. Probabifity of successful packet synchronization. Probabffity that a transmitted packet is successfully received and is not redundant, given that it is in channel state i. Number of levels in Weldon s ARQ scheme. Channel state transition probability corresponding to reversed Markov chain. Smallest time interval between successive start-of-transmission times for data packets. Tij,im or Tik,1mn Td U w System (joint channel-protocol) state transition probabffity. Round-trip propagation delay over channel. System (joint channel-protocol) state. Retransmission delay parameter, measured in slots. Retransmission delay parameter, measured in service cycle periods. W Total frequency bandwidth available for both the forward and feedback channels. W1, W2 Frequency bandwidth of forward, feedback channel. Xli

15 Acknowledgment The format of this thesis is based on the Master s thesis of Victor Wong, who gratefully acknowledges the assistance of William Cheung in the formatting of his thesis. I would like to thank my fellow colleagues, for all their help and their company. While it would take too much space to list the names of all these people, four individuals deserve special mention for generously imparting their vast knowledge of the UNIX operating system and the various software packages that were needed to get the job done. Ed Casas and Ron Jeffery helped me get through many obstacles at the start of the program. Fortunately for me, I have always been able to count on their veritable successors, Dimitri Bouras and William Cheung, for continued assistance after their departure from the department. Finally, I would like to thank my advisor, Prof. Cyril Leung, for the high quality and optimum quantity of his supervision. The research work for this thesis was supported in part by an NSERC operating grant, a Science Council of B.C. GREAT Award, and by a University of B.C. Graduate Fellowship. xiv

16 Chapter 1 Introduction The primary subject of this thesis deals with the analysis and evaluation of multiplexing and automatic repeat request (ARQ) schemes in multiple-receiver systems with time-varying channels. In addition, two other issues on ARQ are also examined. Briefly, these relate to errors in the feedback channel and a unified procedure for taking into account some of the design trade-offs in an ARQ system. The multiple-receiver system under consideration consists of a transmitter that sends data to several receivers. The quality of the communication channel between the transmitter and each receiver changes over time and depends to a certain extent on the past channel quality. This kind of channel can offer some interesting possibifities in a multicast system, where data intended for particular groups of receivers are sent from a central transmitter. A multiplexer is used to select which group is to be served at a given time. Now if the channel quality of each receiver varies over time, then the multiplexer may be able to improve its transmission efficiency by an adaptive receiver selection scheme that is biased towards serving higher quality over lower quality channels, Such an adaptive scheme is examined in this thesis for a special case of the multicast system, a multiple point-to-point system, where each group contains only one receiver. The applications under consideration are presumed to require that the transmitted data be received without error and in the correct sequence. This requirement is accomplished through the use of an ARQ protocol. The effect of feedback channel errors on ARQ protocol performance is an issue that has not received much attention in the published research literature. It is well known that feedback errors will reduce the protocol s throughput, but the nature and extent of this effect needs to be clarified in greater detail. Analytic and simulation results are presented, giving a quantitative and qualitative characterization of feedback errors under certain assumptions. A modification for reducing the throughput loss due to feedback errors is proposed. It is applicable in general to any continuous ARQ protocol. I

17 Chapter 1. Introduction 2 The design of an ARQ protocol can require decisions on performance and resource requirement trade-offs between different design parameters such as the packet length, as well as coding and modulation schemes. Of interest is the design of good ARQ protocols under power and bandwidth constraints. A description is given of a procedure for taking into account these various parameters, from which the resulting information data bit transmission rate can be calculated, This transmission rate may be viewed as a measure of the capacity of an ARQ system. It can be maximized for certain parameter values, subject to given constraints. Some basic concepts and commonly used terms are discussed in the next section, followed by a section on previous research work in the area, and finally by a section that summarizes the contributions of this thesis, and describes how the rest of the thesis is organized. Li Preliminaries Reliable Data Communication A communication system can be viewed in its simplest form as consisting of a transmitter, a receiver, and a channel over which the transmitter sends information (data) to the receiver. Invariably, the original transmitted data will be corrupted by the channel (because of physical characteristics such as noise and bandwidth limitations, among others) and consequently, may be received in error. For applications such as voice (telephony), FAX and video transmission, there typically is some latitude in the amount of corruption to the received data which would still be subjectively considered acceptable. However, there are other applications, such as file transfer, where the transmitted data must be received without error. For these applications, the communication system must be able to transmit data reliably in order to serve a useful purpose. As this thesis is concerned with reliable data transmission, data without any further qualification will, henceforth, refer to the type with stringent error control requirements. In practice, data transmission cannot ever be completely error-free since there is always the possibifity, however miniscule, that the received data can contain undetected errors. The reason for the occurrence of undetected errors is treated in coding theory (e.g., [1, 2]); issues

18 Chapter 1. Introduction 3 Incoming Data Delivered Data ARQ System / Figure 1.1 Block diagram of an ARQ system. in that area are beyond the scope of this thesis. Hence, the term error will be used to denote only a detected error, unless qualified otherwise. 10t2 FEC and ARQ An error control system can be organized into two general classes depending on whether or not the transmitter retransmits data that have been received in error. In the first class of systems, there is no retransmission, and consequently, some form of error correction coding is typically used to reduce the number of errors in the received data to an acceptable level. Hence, it is commonly referred to as Forward Error Correction (FEC), although it can be thought of as encompassing applications where error correction coding may not be used if the data error rate requirements can already be met without the use of coding. In the second class, the transmitter makes use of information fed back from the receiver to correct detected errors by resending data received in error. The received data is not released to the application at hand until all errors have been corrected. This class is referred to as Automatic Repeat Request (ARQ), reflecting the iterative procedure wherein the receiver essentially requests retransmissions of corrupted data. An ARQ system utilizes two channels between the transmitter and the receiver, one over which the transmitter sends data to the receiver, and another for feedback from the receiver. These are referred to as the forward and feedback channels respectively. A block diagram of a general ARQ communication system is shown in Fig In both FEC and ARQ, the transmitted data must also be delivered to the final destination in the correct order.

19 Chapter 1 Introduction 4 It should be noted that a feedback channel can also be used for purposes other than for sending retransmission requests. Channel quality information can also be sent over the feedback channel, as is done with the adaptive multiplexing scheme (in this thesis) for timevarying channels. Another application that makes similar use of the feedback channel is an adaptive FEC scheme [3], where the transmitter changes the error-correcting capability in accordance with the perceived channel quality. In general, data to be transmitted are usually divided into contiguous blocks which are sent out block-by-block. This is done for reasons as may arise for example, from practical considerations in multiple-access, multiplexing, and networked environments. For purposes of error-control, and with ARQ in particular, this division is done to facilitate the retransmission of data received in error. Each data block is encapsulated by a number of fields to form a packet. Each packet must contain fields for numbering the sequence of packets and for parity bits of the error-detection code so that the data can be delivered ( released from the receiver) without error and in the correct sequence. There may also be fields for other uses such as packet synchronization and addressing. Transmission time is usually divided into uniform intervals called slots, each of which can accomodate one packet. ARQ protocols fall into three general classes: stop-and-wait (SW), go-back-n (GBN), and selective-repeat (SR) [111. The basic operations of these protocols are typically described as fol lows. First, the round-trip channel propagation delay, N, is defined as the time, measured in packets, between the start of a packet s transmission and receipt of its corresponding acknowl edgment (e.g., as shown in Fig. 1.2 for the case of N = 4). In SW ARQ, the transmitter sends one data packet over the channel and waits for the arrival of its corresponding acknowledg ment, which the receiver sends after the packet has been received and processed. A positive acknowledgment (ACK) is sent if the packet is or has already been received without error. Otherwise, a negative acknowledgment (NACK) is sent back. The transmitter then either retransmits the packet if an ACK was not received, or transmits the next packet otherwise. In GBN and SR ARQ, the transmitter continues to send the next packets in its transmission 1 Also called send-and-wait, reject, and selective-reject respectively.

20 1 Chapter 1. Introduction 5 Receiver N=4 Transmitter Figure 1.2 Channel delay, N. sequence while waiting for the receiver s acknowledgments to return. For this reason, they are called continuous ARQ protocols. With these protocols, it is possible for later pack ets (with higher sequence numbers) to be correctly received ahead of earlier packets in the transmission sequence (i.e., received out-of-sequence ). With GBN ARQ, NACKs are sent for these out-of-sequence packets. Hence, whenever a leading packet is received in error, the transmitter has to resend not only the leading (or first outstanding ) packet (FOP), but also the next N packets. With SR ARQ, the receiver has a resequencing buffer for storing out-of-sequence but correctly received packets before they can be released to the destination in the correct order. ACKs are returned for each of these packets. If however, there is no space for storing an incoming out-of-sequence packet in the buffer (a condition called buffer overflow ), that packet is lost and a NACK is sent back. Hence, the transmitter resends only packets that are received in error or are lost due to buffer overflow. In this thesis, a data packet is said to be completed if it has been either released from the receiver or buffered and pending release from the resequencing buffer (i.e., there is no need to retransmit it). A transmitted packet that has not yet been completed is said to be outstanding. The decision as to whether FEC or ARQ is used typically depends on constraints imposed by the application. In general, one wants a communication system to deliver data as reliably and as efficiently as possible. This would usually point to the use of an ARQ protocol. However, for applications such as real-time voice/video and some aspects of deep space data-collection telemetry, the retransmission iterations involved with ARQ may result in unacceptably long or uncertain time delays in the delivered data, In such cases, one is forced

21 Chapter 1. Introduction 6 to use FEC and to design the system so that data is delivered at some acceptable error rate. FEC can also be used in conjunction with ARQ, resulting in what is called a hybrid ARQ (HARQ) protocol, where error correction is used to reduce the number of retransmissions. There are two common types of HARQ, namely, Type I and Type II. With Type I HARQ, parity bits for error-correction are sent with the (re)transmitted packet. With Type II HARQ, the packet is transmitted first without error correction, and parity bits are sent during subsequent retransmissions. Obviously, there can be combinations between these two types. t1,3 Point-to-Multipoint ARQ The discussion so far has described an ARQ system where one transmitter sends data to one receiver. Such an arrangement is usually called a point-to-point system. Another, more general, arrangement consists of one transmitter which broadcasts to several receivers (as shown in Fig. 1.3), where the requirements of error control and sequential delivery of data now extend to all receivers. This is called a broadcast or point-to-multipoint system. Each receiver processes received packets and sends back acknowledgments in the same way as in a point-to-point system. However, the transmitter s operation changes somewhat on account of the multiple receivers. For each outstanding packet, an ACK is expected from each receiver. For any transmitted packet, a receiver is said to be outstanding if its corresponding ACK has not yet been received. The acknowledgment status of outstanding packets for each receiver is stored by the transmitter in an ack-outstanding list. The retransmission procedure depends on what information is stored in the ack-outstanding list. Suppose the list can store acknowledgment status information from all receivers for the first m outstanding packets, o m N. Then ACKs are expected from only the outstanding receivers for the first m packets, and from all receivers for retransmissions of the remaining packets (because their acknowledgment status is not known), Memoryless, limited memory and full memory systems are terms used respectively for the cases where m = 0 (an ack-outstanding list is not used), 0 < m < N, and m = N.

22 Chapter 1. Introduction 7 1,1.4 Multiplexing and Multicast Systems The point-to-multipoint system itself can be generalized into a multicast system, where multiple point-to-multipoint ARQ sessions operate in parallel among sets of multiple receivers. Each set, or multicast group, can consist of anywhere from one receiver to all the receivers in the system. More than one multicast group can be active at any given time and a receiver may also belong to more than one active group (i.e., the groups may overlap each other). A general multicast configuration is shown in Fig ARQ transactions operate independently between groups. A multiplexer is used to allocate system bandwidth among multicast groups if several of them are operating simultaneously. Bandwidth allocation is Receivers I ii. II,I.0 e I... Figure 1.3 Point-to-multipoint system.

23 Chapter 1. Introduction 8 typically done either in the frequency domain (e.g., each group is assigned a frequency band) or in the time domain (e.g., packet transmission time is divided into slots, which are assigned in a particular way so that there is transmission to no more than one group at any given slot). 1,2 A Brief Summary of Related Work ARQ systems have been the subject of research for a long time. The following discussion is a summary of some of the preceding work. It serves as a starting point for identifying both new topics to examine as well as issues which have not yet been adequately addressed. E Receivers Multicast Group I Figure 1.4 General multicast system.

24 Chapter 1. Introduction 9 The basic concept of ARQ is so simple that it must have arisen with the advent of data communications, For example, HF teleprinter systems employing ARQ were used since the late 1930 s [2]. An early survey of ARQ schemes appears in [4]. 1,2.1 Analysis The performance of the standard ARQ protocols has been examined in a number of papers. Queueing statistics for standard GBN and ideal selective repeat (ISR) ARQ are analyzed in [5, 6]. Some design issues for SR ARQ protocols are discussed in [7], while the throughput performance of a finite-buffer SR ARQ scheme has been investigated in [8]. Analysis of the resequencing buffer occupancy and delay (for SR ARQ) can be found in [9 11], Recently, signal flow graphs have been used to analyze the throughput and delay of ARQ protocols [12]. Analysis of multi-channel ARQ protocols can be found in [11, 13]. In a multi-channel system, packets are sent over parallel ARQ channels. ARQ protocols are typically analyzed for equilibrium conditions that extend over an infinite duration. Also of interest is the performance of ARQ protocols over the period when a finite number of packets are to be completed [12, 14]. Other assumptions that are often made include error-free feedback channels and a stationary, uncorrelated channel error process. A review of the previous work done on error-free feedback channels is given in Chapter 2, Non-stationary errors are typically modeled by a Markov process over a set of channel states which correspond to either a bit error (or packet error) probability [15 17], or the packet error events themselves [18, 19]. Other approaches have used a Rayleigh fading channel model [20] or line-gap functions [16] Systems When ARQ is used over packet-switched networks, transmitted packets may have to travel through several nodes between the source and destination. Some papers that have evaluated ARQ protocols in these enviroments include [21 23]. A new window protocol for acknowledging groups of packets is proposed in [24]. ARQ schemes designed for use in half duplex transmission environments have also been analyzed [25]. In [261, the performance of SR ARQ is evaluated for the IEEE Type-2 logical link protocol. Other issues related to

25 Chapter 1. Introduction 10 networking can be found in [27]. ARQ protocols have also been analyzed for multiplexed [28] as well as TDMA [29] environments Multi-copy Transmission Many schemes for improving the performance of ARQ protocols have been proposed. In one general method, the transmitter sends multiple copies of the same packet pre-emptively instead of sending only one copy of each packet and waiting for the acknowledgment. Sastry [301 has examined the use of multiple-copy transmission for SW ARQ, and has proposed a modification to GBN ARQ, where the FOP is sent repeatedly (i.e., stutter mode) when it has to be retransmitted. Another modification to GBN ARQ makes use of some buffering capacity at the receiver [31], Towsley [32] has analyzed the performance of a stutter GBN protocol in a system where new packets enter according to an arrival process. The last transmitted packet is sent repeatedly when the queue is idle (i.e., while there are no incoming packets to transmit) and when there are no packets to retransmit. The earliest paper to propose a non-stutter multiple-copy scheme appears to be [331, which considers the case of GBN ARQ. An adaptive multiple-copy scheme for finite-buffer SR ARQ was proposed by Weldon [34] in order to reduce the number of packets lost due to buffer overflow. Further results on its analysis and optimization have been done in [35, 361. There have been earlier variations to SR ARQ, which avoid buffer overflow by switching to stutter transmission or GBN ARQ operation when buffer overflow is imminent [37]. Multiple-copy ARQ schemes are also discussed in [38 40]. Copies of packets received in error can also be combined in order to reduce the number of unsuccessfully decoded packets. This method is usually referred to as code combining, memory ARQ or multiple copy decoding (MCD), and may also be used in conjunction with soft-decision decoding. Some papers that discuss this approach include [41 51]. 1,2.4 Type-I HARQ Virtually any kind of error-correction code can be used to implement a type-i HARQ protocol. Some of these schemes have been described in a number of papers. Majority-logic

26 Chapter 1. Introduction 11 decoding of convolutional codes can be used for high-speed implementations at the expense of coding gain [52]. This approach can also be used with a packet combining scheme [53]. Adaptive type-i HARQ schemes have been proposed for both RS [54, 551 and punctured convolutional codes [31. An adaptive scheme that uses concatenation with multiple-copy transmission and soft-decision decoding has been proposed in [51], The amount of coding used for error correction can also be adjusted by using estimates of the channel quality rather than basing it on the number of retransmissions. This approach has been used in conjunction with both RS [54, 55] and convolutional codes [3] Type-Il HARQ A number of type-il HARQ schemes have been proposed. In [56], two schemes are discussed, one involving the use of convolutional codes; in the other, a packet is divided into sub-blocks, each of which is encoded with an rate-i /2 code that has a Reed-Muller structure. Lin and Yu [571 have proposed a class of half-rate invertible codes suitable for HARQ. In [58], a class of linear codes suitable for parity retransmission was proposed. The same decoder structure is used for decoding codewords formed from successively catenated parity bits. The use of this scheme for non-stationary channels has been analyzed in [59]. A similar concept, wherein Hamming codes are used in a cascaded manner to encode sub-blocks comprising the data frame, is proposed in [60]. One way of using the more standard coding schemes for adaptive parity retransmission is to use some form of concatenation as described in [611 for extended BCH and Hamming codes. Another way is to send in the first transmission only a subset of the parity bits from the original code along with the information bits (i.e., the codeword is punctured ), and to send the remaining parity bits in subsequent retransmissions [62, 63]. Such a procedure can be used if the bits are punctured such that the code is rate-compatible. The use of this approach has been subsequently discussed in [641 (for convolutional codes) and [651 (for RS codes). 1,2,6 Code Combining The use of maximum-likelihood and soft-decision decoding for code combining has been

27 Chapter 1. Introduction 12 discussed in [45]. Code combining can also be used in conjunction with sequential decoding of convolutional codes [661. In [67], a partial-retransmission variation is described, where sub-blocks of the encoded sequence are sent and combined with the received packet. Some combining schemes have been considered for use in both type-i and type-il HARQ with Viterbi decoding of convolutional codes [68 72]. Type-Il HARQ schemes based on the use of punctured convolutional codes have been proposed in [64, 72 74]. It should be noted that multiple-copy transmission schemes can be viewed as implemen tations of a repetition code. In that sense, it could be argued that they can be viewed as type-i HARQ schemes. Likewise, any scheme where the receiver combines retransmitted packets could be viewed as a type-il HARQ protocol, since the retransmitted packets could be con sidered as parity bits of a repetition code Optimum Packet Length The packet length is a parameter that can affect the performance of ARQ systems. In [75], the optimum packet size that minimizes the expected amount of transmission time required to complete a message (counting retransmissions as well as acknowledgments) is determined after taking into account factors such as the message length distribution, channel error characteristics, as well as overhead in the data and acknowledgment packets. An optimization along similar lines is also given in [76]. With HARQ, there is a trade-off between improved error-correcting capability and overhead from parity bits. This issue has been examined for the case of BCH codes in [77]. Some adaptive schemes that change the packet length according to prevailing channel conditions have also been proposed [78, 79] Point-to-multipoint ARQ Point-to-multipoint ARQ protocols have been the subject of fairly recent research work. A number of protocols for broadcast applications have been proposed and analyzed. Some schemes use a batched acknowledgment technique, where packets are grouped into frames, and acknowledgments are sent back for each received frame, each of which identifies which packets in the frame have been received correctly. These have been proposed in [80] and [81]

28 Chapter El. Introduction 13 for broadcast SW and GBN ARQ respectively. Two full-memory GBN ARQ protocols were pro posed by Mase [82] for satellite applications. One scheme uses end-to-end acknowledgments (between ground stations), while another uses a tandem arrangement, where ARQ is used on both the uplink as well as the downlink. In [83], the GBN ARQ protocol is examined for differ ent amounts of memory in the transmitter s ack-outstanding list. Memoryless and full-memory systems are also discussed in [84] for both GBN and ISR ARQ. A broadcast ARQ scheme in which ACKs are not sent back [851 has been proposed for use in mobile radio environments where receivers may be subject to deep fades due to shadowing, as well as in multiple-access feedback channels where collisions can occur among the receivers acknowledgments. Multiple-copy transmission of packets can also be used to improve the performance of GBN ARQ for point-to-multipoint channels [86 88]. Broadcast versions of Weldon s SR ARQ scheme have been examined in [89, 90, 361. Delay and occupancy statistics at the resequencing buffer for multiple receiver ISR ARQ systems are analyzed in [91]. Ammar [92] has proposed a scheme for improving the throughput of broadcast ARQ protocols by splitting the receivers into multicast groups. HARQ schemes for broadcast applications have also been considered. These schemes involve the use of convolutional codes [901 as well as concatenated codes (using shortened Hamming codes) [17]. 1.3 Summary of Contributions New results presented in this thesis include the following: 1. A simple method for reducing the deleterious effects of feedback errors on the throughput performance of continuous ARQ protocols by using complete receiver state information feedback and by modifying the transmitter s retransmission procedure. 2. An analytic procedure for the unified treatment of trade-offs in various design options (e.g., modulation and coding schemes). 3. Throughput analysis of multiplexing and ARQ schemes for non-stationary, multiple point to-point systems with time-varying error processes. The effects of state-estimation errors and feedback errors have also been included in the analysis. Furthermore, the modified re

29 Chapter 1, Introduction 14 transmission procedure in item 1 is also extended to this system. An adaptive multiplexing scheme is proposed. This scheme is optimal when used with TSR ARQ. The remainder of this thesis is structured based on the items listed above. The more fundamental issues are addressed first, with feedback errors in Chapter 2, and the unified design procedure in Chapter 3. Following these, the throughput of the multiplexed system is analyzed in Chapters 4 and 5. The corresponding numerical results are discussed in Chapter 6. Some general concluding remarks are then given in Chapter 7.

30 Chapter 2 Some Aspects of ARQ Throughput Performance in the Presence of Feedback Errors This chapter discusses the effect of feedback errors in a stationary point-to-point channel under some feedback information assumptions. It is shown that the deleterious effects of feedback errors on the throughput of continuous ARQ protocols can be greatly reduced by a simple modification in the retransmission operation, provided that the complete state of the receiver is sent back with each acknowledgment. 2.1 Introduction In many papers that analyze the performance of ARQ protocols, the feedback channel is assumed to be error-free (e.g., [30 32, 15, 37, 57, 34, 35, 39, 38, 18, 86, 68, 69, 90, 71, 73]). This assumption is typically made in order to simplify the analysis or the presentation of results. Some recent papers have included the effect of feedback errors in the performance analysis. As a first approximation, an ACK or NACK received in error is treated as though a NACK was received. Hence, a data packet sent over the forward channel is considered to have been successfully transmitted only if its corresponding acknowledgment is also received without error. This assumption was used in [19], and is referred to as the simple product approximation in this thesis. In [12], a modified GBN ARQ protocol 2 is considered, where the receiver sends back a sequence number, i, along with the ACK or NACK to indicate respectively that all packets up to and including the ith or (i 1)th packet have been correctly received. The information contained in the acknowledgment can be used to update the status of a previously transmitted packet whose acknowledgment was lost. It is assumed in these two papers that an error in the feedback channel can only erase an ACK or NACK. In [59], a different feedback error process is considered, where an error changes an ACK into a NACK, or vice versa (i.e., the error is not detected). When a NACK is received as an ACK, a data 2 As implemented in HDLC. 15

31 Chapter 2. Some Aspects of ARQ Throughput Performance in the Presence of Feedback Errors 16 packet may be lost unless the transmitter realizes the error and retransmits the packet. On the other hand, an ACK incorrectly received as a NACK will cause a spurious or redundant retransmission of a correctly received packet. This chapter expounds on some aspects of feedback errors mentioned in [931. A model for ARQ protocols is developed and the nature of the feedback error process is examined in Sections 2.2 and 2.3. Following this, a modification to the standard GBN and SR ARQ protocols is proposed, analyzed, and compared with other schemes in Sections 2.4, 2.5 and 2.6. In this study, the following assumptions are made. 1. Each acknowledgment packet contains error-detection bits such that it can be assumed that all errors in the feedback channel are detected. Hence, feedback errors can only erase acknowledgments. 2. Packet errors in the forward and feedback channels occur independently within each channel as well as between the channels. The error rates for both channels are assumed to be stationary. 3. New packets are always available to be sent out by the transmitter. 2,2 A Buffer-Constrained Model for ARQ Protocols The feasibffity of an ARQ protocol is constrained by both its processing complexity as well as the available packet buffer capacities at the transmitter and receiver. The issue of processing complexity is difficult to quantify concisely, and may depend on the state of computing technology as well as on implementation issues and the desired data transfer rate. Hence, the following discussion will focus on the buffer capacity requirements of an ARQ protocol. At the transmitter, a retransmission buffer is used for storing outstanding (i.e., transmitted but unacknowledged) packets for possible retransmission. At the receiver, a resequencing buffer is used for storing packets that have been successfully decoded but still cannot be released in the correct order until other packets ahead in the sequence are successfully received. If processing complexity is not considered, the three basic ARQ protocols (SW, GBN, and SR) can be classified by the available buffer capacities. Let B1 and B2 denote respectively the

32 Chapter 2. Some Aspects of ARQ Throughput Performance in the Presence of Feedback Errors 17 retransmission and resequencing buffer capacities (measured in packets). Suppose B1 = 1 and B2 = 0. As a consequence of the restriction on B1, the transmitter cannot have more than one outstanding packet at any given time. Hence, the transmitter has to stop (from sending the next packet) and wait for the receiver s feedback (in response to the transmitted packet) before either retransmitting the packet or sending the next one. This is the operation of SW ARQ, Now suppose that B2 = U but B1 = N, where N is the propagation delay of the channel, measured in packets, from the start of packet transmission to the point when the corresponding acknowledgment is expected to have been received and processed. As a result of increasing B1 from 1 to N packets, the transmitter can now send the next N 1 packets (in the transmission sequence) during the intervening time before receiving the acknowledgment for the leading packet. If the leading packet is not successfully received, the next N 1 packets cannot be released by the receiver even if they have been received without errors because they would not be in the correct order. Moreover, they will have to be dropped because there is no space for holding them. Hence, all N packets have to be retransmitted whenever a leading packet is received in error, resulting in GBN ARQ. By using a resequencing buffer (B2 > 0), the number of dropped packets can be reduced, resulting in an attendant reduction in the number of retransmissions. This leads to the SR ARQ protocol, where successfully received but outof-sequence packets need not be retransmitted if they can be stored in the resequencing buffer before being released in the correct order. Buffer capacities for the three protocols are depicted in Fig The TSR ARQ protocol is the limiting case as B2 * cc. In TSR ARQ, resequencing buffer overflow does not occur (as there is always space for buffering packets), so that only packets received in error are retransmitted. There has been some interest in the analysis of finite-buffer SR ARQ protocols [34, 35, 42], By using Weldon s bound [341 however, it can be shown that in many cases, the throughput attainable under TSR ARQ can be approached very closely by using SR ARQ with a resequencing buffer that is not enormously large. 2.3 The Feedback Channel The feedback channel provides a means by which the receiver can send information back

33 Chapter 2. Some Aspects of ARQ Throughput Performance in the Presence of Feedback Errors 18 L Retransmission: Chann& Transmitter Feedback IARQ System SWARQ Receiver Resequencng I [EELZ GBNARQ N LIEIEI SR ARQ liii Figure 2.1 Buffer capacities required for some ARQ protocols. for use by the transmitter. For example, the information may take the form of acknowledgment packets to inform the transmitter of the completion status of transmitted data packets. Based on this information, the transmitter attempts to deduce the receiver s state, and adjusts its transmission sequence accordingly. There are many possible acknowledgment schemes. For the purposes of analysis, these schemes can be differentiated on the basis of the amount and frequency of the information sent back. Before proceeding further, some clarification of the terminology needs to be made. Con sider a system where data packets are also being transmitted in the opposite direction. The feedback may be sent either separately, or piggy-backed over the data packets. In either case, the same physical charmel is used for sending both data packets and acknowledgments,