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Design and Performance Optimization

of Wireless Network Coding for Delay

Sensitive Applications

Mohammad Esmaeilzadeh Fereydani

A thesis submitted for the degree of

Doctor of Philosophy

The Australian National University

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Declaration

Except where otherwise indicated, this thesis is the result of my own original work under the guidance and supervision of Associate Prof. Parastoo Sadeghi during the period of my PhD degree at the Australian National University. Most of the results in this thesis have been published in refereed journals and at international conferences. They are as follows:

1. M. Esmaeilzadeh and P. Sadeghi, Optimizing completion delay in network coded sys-tems over TDD erasure channels with memory.International Symposium on Communi-cations and Information Technologies (ISCIT), Gold Coast, Australia, 2-5 October 2012. 2. M. Esmaeilzadeh, N. Aboutorab and P. Sadeghi, Guaranteeing QoS in network coded TDD satellite broadcast systems with hard delivery deadline. IEEE International Sym-posium on Personal, Indoor and Mobile Radio Communications (PIMRC), London, UK, 8-11 September 2013.

3. M. Esmaeilzadeh, N. Aboutorab and P. Sadeghi, Joint optimization of throughput and packet drop rate for delay sensitive applications in TDD satellite network coded systems.

IEEE Transactions on Communications, vol. 62, no. 2, February 2014.

4. M. Esmaeilzadeh and N. Aboutorab, Inter-session network coding for transmitting multi-ple layered streams over single-hop wireless networks.IEEE Information Theory Work-shop (ITW), Hobart, Australia, 2-5 November 2014.

5. M. Esmaeilzadeh, P. Sadeghi and N. Aboutorab, Random linear network coding for wireless layered video broadcast: General design methods for adaptive feedback-free transmission.IEEE Transactions on Communications, Accepted, November 2016.

Mohammad Esmaeilzadeh Fereydani 1 December 2016

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Acknowledgments

First and foremost, I thank God, the Almighty, for his countless blessings in my life. I am very blessed to have interacted with and learnt from many wonderful people throughout my life. I would like to thank all those whose kind support and assistance made this thesis possible:

I would like to express my very special appreciation to my supervisor, Associate Prof. Parastoo Sadeghi for her incredible support, and continuous guidance and encouragement dur-ing my candidature at ANU. I am very grateful to her for helpdur-ing me in learndur-ing the various skills of academic research and for her valuable contributions and suggestions towards my research and publications. I feel honored to had the opportunity to work under her supervision. I would like to thank Dr. Neda Aboutorab for her great help and support. I am very grateful to Neda for always being open to in-depth discussions and for going carefully through my publication drafts. I am also grateful to Prof. Rodney A. Kennedy, Prof. Richard Hartley, Dr. Salman durrani and Dr. Bradley Treeby for their support and advices at different stages of my PhD. In addition, I am thankful to Dr. Hulya Seferoglu and Dr. Sameh Sorour for their inspiration.

Many thanks to current and past members of the Applied Signal Processing group at the Australian National University, including but not limited to Yibeltal, Mohammad Karim, Akra-mus, Shahriar, Zubair, Abbas, and Xiang for creating a friendly and pleasant working environ-ment. I am also indebted to all my dear friends at Canberra, especially Mohammad Najafi, for making the past years so enjoyable.

I would like to thank my sources of financial support. Firstly, I would like to acknowl-edge the Australian Research Council (ARC) for providing the APA(I) scholarship. Moreover, I would like to thank my supervisor, the Australian National University and the School of Engineering for their financial support, which allowed me to attend several conferences.

Last, I wish to express my deepest gratitude to my family. This thesis would not be possible without their continuous love and support. I am extremely grateful to my parents to have sacrificed themselves to give me the best of everything. I also convey my thanks to my brother for taking care of everything back home during my absence. My special thanks go to the love of my life, Sarah, who has been very supportive, patient and encouraging during these years.

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Abstract

Over the past decade, network coding (NC) has emerged as a new paradigm for data commu-nications and has attracted much popularity and research interest in information and coding theory, networking, wireless communications and data storage. Random linear NC (RLNC) is a subclass of NC that has shown to be suitable for a wide range of applications thanks to its desirable properties, namely throughput-optimality, simple encoder design and efficient operation with minimum feedback requirements. However, for delay-sensitive applications, the mentioned advantages come with two main issues that may restrict RLNC usage in prac-tice. First is the trade-off between the delay and throughput performances of RLNC, which can adversely affect the throughput-optimality of RLNC and hence the overall performance of RLNC. Second is the usage of feedback, where even if feedback is kept at minimum it can still incur large amount of delay and thus degrade the RLNC performance, if not optimized properly. In this thesis, we aim to investigate these issues under two broad headings: RLNC for applications over time division duplexing (TDD) channels and RLNC for layered video streaming.

For the first class of problems, we start with the reliable broadcast communication over TDD wireless channels with memory, in the presence of large latency. Considering TDD chan-nels with large latency, excessive use of feedback could be costly. Therefore, joint optimization of feedback rate and RLNC parameters has been studied previously for memoryless channels to minimize the average transmission time for such settings. Here, we extend the methodology to the case of channels with memory by benefiting from a Gilbert-Elliot channel model. It is demonstrated that significant improvement in the performance could be achieved compared to the scheme which is oblivious to the temporal correlations in the erasure channels.

Then, keeping our focus on network coded TDD broadcast systems with large latency, we consider delay sensitive applications and study the issue of throughput and packet drop rate (PDR) optimization as two performance metrics when the transmission time is considered fixed. We propose a systematic framework to investigate the advantage of using feedback by comparing feedback-free and feedback schemes. Furthermore, the complicated interplay of the mean throughputs and PDRs of users with different packet erasure conditions is discussed.

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x

Then, to better analyze the throughput performance of the proposed feedback-free scheme, we formulate the probability and cumulative density functions of users’ throughputs and utilize them to investigate the problem of guaranteeing the quality of service. Finally, it is shown that the optimized feedback-free RLNC broadcast scheme works close enough to an idealistic RLNC scheme, where an omniscient sender is assumed to know the reception status of all users immediately after each transmission.

For the second class of problems, we consider transmitting layered video streams over het-erogeneous single-hop wireless networks using feedback-free RLNC. For the case of broad-casting single video stream, we combine RLNC with unequal error protection and our main purpose is twofold. First, to systematically investigate the benefits of the layered approach in servicing users with different reception capabilities. Second, to study the effect of not using feedback, by comparing feedback-free schemes with idealistic full-feedback schemes. To this end, we consider a content-independent performance metric and propose a general framework for calculation of this metric, which can highlight the effect of key parameters of the system, video and channel. We study the effect of number of layers and propose a scheme that selects the optimum number of layers adaptively to achieve the highest performance. Assessing the proposed schemes with real H.264 test streams, the trade-offs among the users’ performances are discussed and the gain of adaptive selection of number of layers to improve the trade-offs is shown. Furthermore, it is observed that the performance gap between the proposed feedback-free scheme and the idealistic scheme is small and the adaptive selection of number of video layers further closes the gap.

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Contents

Acknowledgments vii

Abstract ix

1 Introduction 1

1.1 Motivation . . . 1

1.2 Thesis Contributions . . . 3

1.2.1 RLNC for Applications over TDD Channels . . . 3

1.2.1.1 RLNC for TDD Erasure Channels with Memory . . . 4

1.2.1.2 RLNC for Delay Sensitive Applications over TDD Channels 4 1.2.2 RLNC for Layered Video Streaming . . . 6

1.2.2.1 RLNC for Broadcasting of Layered Video . . . 6

1.2.2.2 RLNC for Transmitting Multiple Layered Video Streams . . 7

1.3 Thesis Outline . . . 8

2 Background and Related Work 9 2.1 Network Coding . . . 9

2.1.1 Fundamental Studies . . . 10

2.1.2 Random Linear Network Coding . . . 11

2.1.3 Applications of Network Coding . . . 12

2.2 Practical Issues in Implementation of Network Coding . . . 13

2.3 Delay Analysis of Network Coding . . . 16

2.4 Network Coding for Delay Sensitive Applications . . . 18

2.5 Network Coding for Video Streaming . . . 19

3 Random Linear Network Coding for Time Division Duplexing Channels 23 3.1 Chapter Goals . . . 23

3.2 Random Linear Network Coding . . . 23

3.2.1 Coding and Decoding . . . 24

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xii Contents

3.2.2 Effect of Field Sizeqon RLNC Decoding . . . 26

3.2.3 Feedback Challenges for TDD Channels with Large Latencies . . . 27

3.3 New Case Study: Optimizing RLNC Completion Time and Throughput for TDD Erasure Channels with Memory . . . 28

3.3.1 System Model . . . 29

3.3.1.1 GEC Model for Channels with Memory . . . 30

3.3.1.2 Transmission Scheme . . . 31

3.3.1.3 Completion Time and Throughput Performance Metrics . . 32

3.3.2 Formulation and Optimization of Performance Metrics . . . 34

3.3.2.1 Completion Time . . . 34

3.3.2.2 Throughput . . . 37

3.3.3 Numerical Results . . . 38

3.3.3.1 Parameters Values . . . 38

3.3.3.2 Mean Completion Time . . . 38

3.3.3.3 Throughput . . . 41

3.3.3.4 Last CS Estimation . . . 43

3.4 Summary . . . 43

4 Random Linear Network Coding for Delay Sensitive Applications over TDD Satel-lite Channels 45 4.1 Chapter Motivations and Goals . . . 45

4.2 System Model . . . 48

4.2.1 RLNC and Systematic RLNC . . . 48

4.2.2 One-round (Feedback-free) and Two-round (with Feedback) Transmis-sion Schemes . . . 49

4.2.3 Throughput and Packet Drop Rate (PDR) Performance Metrics . . . . 53

4.3 Formulation and Joint Optimization of Mean Throughput and PDR . . . 54

4.3.1 Single-user Case . . . 54

4.3.1.1 One-round RLNC Scheme . . . 54

4.3.1.2 One-round SRLNC Scheme . . . 56

4.3.1.3 Two-round RLNC Scheme . . . 56

4.3.1.4 Two-round SRLNC Scheme . . . 58

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Contents xiii

4.3.2 Multi-user Case . . . 62

4.3.2.1 Scenario I, MaximizingE{η}of a Single User Subject to a Constraint on its PDR . . . 63

4.3.2.2 Scenario II, Maximizing the Mean of Users’E{η}Subject to Constraints on PDR of all Users . . . 63

4.3.2.3 Scenario III, Maximizing the Mean of Users’E{η}Subject to a Constraint on the Mean PDR . . . 64

4.3.2.4 Scenario IV, Maximizing the Mean of Users’E{η}Subject to a Constraint on the Geometric Mean PDR . . . 64

4.3.3 Baseline Schemes . . . 64

4.3.3.1 Round Robin (RR) . . . 65

4.3.3.2 LT Coding Scheme . . . 66

4.3.3.3 Idealistic SRLNC (ISRLNC) . . . 66

4.3.4 Numerical Results . . . 68

4.3.4.1 Parameter Values . . . 69

4.3.4.2 One-round Schemes versus Two-round Schemes- Single-user Case . . . 69

4.3.4.3 One-round RLNC and SRLNC Schemes- Single-user Case . 71 4.3.4.4 One-round SRLNC Scheme- Multi-user Case . . . 74

4.3.4.5 One-round SRLNC Scheme- Broadcasting with VariableM andq . . . 76

4.3.4.6 Comparing One-round Schemes- Broadcasting with Vari-ableM andq . . . 77

4.4 Guaranteeing Quality of Service (QoS) . . . 79

4.4.1 Formulations of Throughput Distribution and PDR . . . 80

4.4.1.1 Single-user Case . . . 80

4.4.1.2 Multi-user Case . . . 81

4.4.2 Numerical Results . . . 82

4.4.2.1 Single-user Case . . . 83

4.4.2.2 Multi-user Broadcast Case . . . 84

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xiv Contents

5 Random Linear Network Coding for Broadcasting of Layered Video 91

5.1 Chapter Motivations and Goals . . . 91

5.2 System Model . . . 94

5.2.1 Expanding Window RLNC . . . 95

5.2.2 Transmission Schemes . . . 97

5.2.2.1 Feedback-free Scheme . . . 97

5.2.2.2 Full-feedback Scheme . . . 98

5.2.2.3 Uncoded Scheme . . . 98

5.2.3 Theoretical and PSNR Performance Metrics . . . 98

5.3 Formulation of Theoretical Performance Metrics – Single-user Case . . . 100

5.3.1 Feedback-free Scheme . . . 100

5.3.2 Full-feedback Scheme, using Finite Horizon Markov Decision Process 102 5.3.2.1 States . . . 102

5.3.2.2 Actions . . . 103

5.3.2.3 State Transition Probabilities . . . 103

5.3.2.4 Reward and Terminal Reward Functions . . . 104

5.3.3 Uncoded Scheme . . . 105

5.4 Extension to Multi-user Case . . . 106

5.4.1 Feedback-free and Uncoded Schemes . . . 106

5.4.2 Full-Feedback Scheme . . . 107

5.4.3 On the Computational Complexities of Multi-user Schemes . . . 108

5.5 SVC Video Streams and PSNR Calculations . . . 108

5.6 Numerical Results . . . 111

5.6.1 Simple Example Using a Sample GOP . . . 112

5.6.2 Results for Single-user Case using Real Layered Video Streams . . . . 114

5.6.3 Results for Multi-user Case using Real Layered Video Streams . . . . 117

5.6.3.1 General Case . . . 117

5.6.3.2 Performance Trade-offs and Fairness . . . 120

5.7 Discussion on Other H.264/SVC Scalability Types . . . 122

5.7.1 Spatial Scalability . . . 123

5.7.2 Spatial and Temporal Scalabilities . . . 123

5.7.3 Quality Scalability . . . 124

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Contents xv

6 Random Linear Network Coding for Transmitting Multiple Layered Video Streams127

6.1 Chapter Motivations and Goals . . . 127

6.2 System Model . . . 128

6.2.1 Inter-session RLNC . . . 129

6.2.2 Transmission Schemes . . . 130

6.2.3 Performance Metric . . . 130

6.3 Formulation of Theoretical Performance Metric . . . 131

6.4 Numerical Results . . . 134

6.5 Summary . . . 137

7 Conclusion 139 7.1 Thesis Contributions . . . 139

7.2 Future Work . . . 140

A Pareto Optimal Solutions 143

B Finite Horizon MDP 145

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List of Figures

2.1 The butterfly network. A message is represented by two bitsaandband the source wants to multicast the message to receivers R1 and R2. In a scenario using NC, V transmits a combination of bits, i.e.,ab. . . . 10 2.2 The probability of decoding all theM packets in a generation, whenNs=αM

RLNC packets are transmitted. Packet erasure probability is assumed asPe=0.1. 15 3.1 Markov chain for rDOF reduction in RLNC decoding. At statek, a successful

reception of an independent packet leads to a state transition to statek−1. . . 26 3.2 Simplistic examples of a sender transmitting data packets to a receiver and

receiving feedback packets from the receiver: (a) full duplex channel with latency of Trt/2, (b) TDD channel with latency of Trt/2, and (c) idealistic full duplex channel with zero latency. . . 27 3.3 A two-state first-order Markov chain corresponding to the GEC model; State

transition probabilities are shown. . . 31 3.4 Block diagram for complete transmission of blocks ofM data packets using

RLNC over TDD erasure channels with memory. The steps that are different to the ones in [27] are highlighted in blue. The feedback has the information to updateiandX.X∈{B, G}andNi,Xi. . . . 32 3.5 Markov chain representation of the RLNC schemes with infrequent feedback.

In (a), states show the rDOF, i.e. the number of required coded packets to decode all the packets in a block. In (b), in addition to rDOF, states show the last channel state too. . . 35 3.6 A schematic for the computation ofPGB(m, N). Here we have considered

PeB =1andPeG=0. Hence,PGB(0,1)andPBB(0,1)become zero. . . . 37

3.7 Mean completion time for transmission ofMdata packets in an erasure chan-nel with memory. Two different chanchan-nel conditions (πb =0.05andπb =0.2) are considered. . . 39

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xviii LIST OF FIGURES

3.8 Optimum values for Ni,B andNi,G that minimizeTM. πb = 0.05and other parameters are similar to those in Fig. 3.7. Two instances with the rDOF equal to 3 and 10 are shown. . . 40 3.9 Packet-level state transition probabilities and the correspondingµandπb for

PebitB =0.2506,PebitG =0.0057,bbit ≃4.66×10−6 andgbit ≃4.19×10−5. PeB

andPeGare considered to be 1 and 0, respectively. Therefore,πbis the average

PER as well. . . 42 3.10 Throughputηversusnfor three different values ofM. For each(M, n)

com-bination,bandgare acquired from Fig. 3.9. Other parameters are similar to those used in Fig. 3.7. . . 42 4.1 Block diagrams for the single-user case one- and two-round SRLNC schemes

and also ISRLNC scheme (#TXs stands forthe total number of transmissions). By considering all theNs packets in (a) to be either RLNC coded, LT coded or uncoded, the diagram for the one-round RLNC, LT and RR schemes will be obtained, respectively. ISRLNC, LT and RR schemes are explained in Sec-tion 4.3.3. . . 51 4.2 Transmission timelines for the single-user case one- and two-round SRLNC

schemes and also ISRLNC scheme. Similar to Fig. 4.1(a), by considering all the Ns packets in (a) to be either RLNC coded, LT coded or uncoded, the diagrams for the one-round RLNC, LT and RR schemes will be obtained, re-spectively. In (c), thesymbols are used to show that the sender has imme-diate knowledge about the success or failure of previous transmissions at these points in time, i.e. right before the transmission of next packet. ISRLNC, LT and RR schemes are explained in Section 4.3.3. . . 52 4.3 State transition diagrams for SRLNC schemes (TX: transmission). States

rep-resent the rDOF. We considerPef b =0in (b) for more clear diagram. . . 57

4.4 Mean throughput versus PDR for the one- and two-round RLNC and SRLNC schemes. Each point corresponds to a set of design parameter(s),{Ns}for the one-round and{Nj, Ns}for the two-round schemes. . . 70 4.5 Mean throughput versus PDR for RLNC and SRLNC schemes for four

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LIST OF FIGURES xix

4.7 Optimum meanE{η} versus field sizeq. . . . 77 4.8 Comparison of the performance metrics for broadcasting scenarios. For

Sce-narios III and IV, the obtained design parameters are {M, Ns} = {14,154}

and {M, Ns} = {53,159} for the RR scheme, {M, Ns} = {42,158} and {M, Ns}={123,160}for the LT scheme, and{M, Ns}={52,161}and{M, Ns}

={151,161}for the ISRLNC scheme, respectively. The design variables for SRLNC scheme were presented in Table 4.3. . . 78 4.9 Throughput distribution of feedback-free SRLNC for transmittingM=20data

packets to a single user. Different PERs (Pe =0.01,0.2and0.5) and feasible values forNs(Ns=25and40) are considered. . . 83 4.10 Throughput distribution for sendingM packets to a single user withPe=0.2,

usingNsfeedback-free SRLNC transmissions. . . 84 4.11 Maximum achievableηthvs.1−PthforN =3,30and300users. The threshold

constraint is considered for two cases: minimum of users’ throughput (min(⋅)) and mean of users’ throughput (mean(⋅)). . . 85 4.12 PDR of the user(s) with the worst PER vs. 1−Pth, for the results shown in

Fig. 4.11. . . 86 4.13 Comparingηthvs. PDR of the user(s) with the worst PER for SRLNC, RR, LT

and ISRLNC schemes withN =30users. . . 88 5.1 System model showing different components and their relations. NT∗is

spe-cific to feedback-free scheme, the immediate feedback and π(s, t) shown in dashed line are specific to full-feedback scheme. Moreover, considering dif-ferent number of layersLand consequently the optimum one,L∗, is specific to opt-layer approaches. These are all discussed in corresponding future sections. 95 5.2 AnL-layer GOP withkℓpackets in theℓ-th layer. Examples of the expanding

windows are shown. . . 96 5.3 An example of states, actions and terminal rewards. Terminal rewards for other

states are zero. . . 103 5.4 A closed GOP with 8 frames, constituted by I, P and B frames. . . 109 5.5 An example of using the nearest decoded frames to conceal the loss of

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xx LIST OF FIGURES

5.6 Optimum expected performance metric versusNtforM =10packets using the feedback-free scheme. Different number of layers and consequently different number of packets per layer are considered as follows:1-layer withK=[10],

2-layer with K = [4,6], 3-layer with K = [4,2,4] and 4-layer with K =

[4,2,2,2]. . . 113 5.7 Throughput performance of the feedback-free RLNC and uncoded schemes

for Nt = 13. The number of points in some curves is naturally limited; for example when L=1, there is only one point on the curve. Each point represents one Pareto optimal policy for the2-user case. ParametersMandKare similar to those used in Fig. 5.6. . . 113 5.8 Average ratio of decoded frames and average PSNR for single-user case using

Foremantest stream. Feedback-free and full-feedback schemes with different number of layers are compared. Values are averaged over 38 GOPs and 100 repetitions. . . 115 5.9 Histograms showing the difference of ηtot between feedback-free schemes

with optimum number of layers and with fixed number of layers for a3-user case using Foremantest stream. Positive ∆ηtot values correspond to higher ηtotvalues of the opt-layer scheme. . . 118 5.10 Histograms showing the difference ofηtotbetween feedback-free and idealistic

full-feedback schemes with optimum number of layers for a3-user case using

Foremantest stream. Positive∆ηtotvalues correspond to higherηtotvalues of idealistic full-feedback scheme. . . 119 5.11 Average PSNR for the multi-user feedback-free and idealistic full-feedback

schemes. Results for opt-layer and2-layer cases are shown. PSNR values are averaged over the38GOPs, the100repetitions and the3users. . . 120 5.12 Trade-off curves, (a) highlighting the advantage of opt-layer approach for the

feedback-free RLNC scheme (b) comparing the feedback-free RLNC and un-coded schemes. Results for three values ofNtare provided. . . 122 5.13 Example GOPs with 4 frames, showing (a) spatial scalability, (b) spatial and

temporal scalability. . . 123 6.1 Example of intra- and inter-session coding windows for 2 independent layered

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LIST OF FIGURES xxi

6.2 An example showing how Algorithm 1 obtains the highest decodable layer. The providedd1 andd2values are prior to running each step. . . 133

6.3 Performance trade-off for inter- and intra-session NC and uncoded UEP scheme for 2 independent layered streams. . . 135 6.4 Performance comparison of inter- and intra-session NC and uncoded UEP

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List of Tables

[image:23.595.121.527.184.751.2]

3.1 A summary of symbols and parameters used in this chapter. . . 33 3.2 Percentage of mean completion time reduction for the examples depicted in

Fig. 3.7, and also for πb = 0.01 and πb = 0.5. This index is calculated as TMmemoryless scheme−Tour scheme

M

TMmemoryless scheme . . . 39 3.3 Percentage of mean completion time reduction for two RTTs of Trt = 20ms

andTrt=500ms and various channel conditions . . . 41 4.1 A summary of symbols and parameters used in this chapter. . . 53 4.2 Optimum value of Ns, along with the arithmetic mean of users’ E{η} and

Pdfor broadcasting scenarios. In Scenario IV, the geometric means are also provided in parentheses. . . 75 4.3 Optimum SRLNC design parameters, and the arithmetic mean of users’E{η}

and Pd for broadcasting Scenarios III and IV. In Scenario IV, the geometric means are also provided in parentheses. . . 77 4.4 Examples of system design parameters for N = 30users andPth = 0.9. Pd

shows the PDR of users withPe =[0.01,0.2,0.5]. PDRs of lower than10−16 are shown asPd=0. Throughput values are in Mega bps (Mbps). . . 87 5.1 Comparing decoding outcome of the EW and NOW approaches for two erasure

patterns examples. . . 97 5.2 A summary of symbols and parameters used in this chapter. Most of the

sym-bols and parameters in the third partition of this table, i.e., A,aℓ, Ssingle, etc.

correspond to the analysis of full-feedback scheme using finite horizon MDP. However, due to space limitations, we have not included the term “finite hori-zon MDP” in their descriptions. . . 99 5.3 Steps for calculation ofLmax(K,NR)usingK=[5,1,2,3]andNR=[4,3,1,3].

Hence, the first two layers can be decoded. . . 101

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xxiv LIST OF TABLES

5.4 Maximum improvement (in the average performance metrics) of full-feedback scheme over feedback-free scheme for various test streams and test setups. Means are also provided in parentheses. . . 116 6.1 Percentage of maximum improvement of inter-session NC over intra-session

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Chapter 1

Introduction

1.1

Motivation

Delivery of high quality, high data rate content over wireless networks has been a constant challenge in many communication systems. This is mainly due to the volatile nature of the wireless medium that poses special constraints on the design of transmission schemes and pro-tocols for such systems. For example, multipath fading and attenuation that exist in a wireless network, along with interference from different radiation sources, can lead to data losses and high packet error rates (PERs). Hence, use of error correction techniques is necessary for reliable data delivery in such networks.

The mentioned issues existing in a wireless network can become even more challenging when combined with the delay constraints imposed by different network topologies and the demands of different traffics. As an example, let us consider the important problem of com-munication over long-latency, low-bandwidth geostationary satellite links [1], which in some cases are the only means of communication, for instance to deliver the Internet to some islands in the Pacific [2]. In such scenarios, a sender will have to wait a full round trip time (RTT) after every transmission to receive the corresponding reception acknowledgments (ACKs)1. Hence, due to long channel latencies, excessive use of feedback to correct erasures will lead to large amount of delays and consequently deteriorates the overall system performance. If the long-latency links are also time division duplexing (TDD), use of feedback will be restricted even further, since the sender has to stop its transmission in order to wait for a feedback. There-fore, feedback-based error correction schemes such as Automatic Repeat reQuest (ARQ) will become very inefficient for such scenarios.

As another example with similar challenges, we can refer to delay sensitive applications such as live multimedia streaming, over wireless networks. For such scenarios, whether the

1

In this thesis, we also use the termsfeedbackandreception reportsto refer to these ACKs.

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2 Introduction

links are long-latency or not, strict playback deadlines restrict the use of frequent feedback, i.e., feedback after every transmission. Hence, designing the reliable transmission schemes that can combat the wireless erasures and at the same time can guarantee a desirable delay performance will be again challenging.

Therefore, for wireless systems similar to the examples discussed above where delay is either an essential system element, a critical design criterion or a key performance metric, error correction techniques that are less (or even sometimes not) dependent on the use of feedback can be more effective. Such techniques are broadly categorized as forward error correction (FEC) codes. In this thesis, our focus will be on random linear network coding (RLNC) [3] that in addition to its error correction capabilities similar to many FEC codes, it can perform efficiently with minimum use of feedback and has other useful properties as will be explained below.

RLNC is a subclass of network coding (NC) [4] that has gained much attention and popu-larity in the last decade thanks to its many desirable characteristics. RLNC, similar to fountain codes (e.g., LT [5] and Raptor [6] codes), is capable of rateless operation, which means for any given set of source symbols, practically limitless set of encoding symbols can be generated. Moreover, RLNC is known to be asymptotically throughput-optimal, which means originalM source symbol can be recovered from any M RLNC encoded symbols, with high probabil-ity. In addition to this, RLNC offers distributed and flexible encoding and decoding opera-tions [7, 8]. For instance, RLNC allows simple extension to general networks by re-encoding at intermediate nodes, where fountain codes can only be applied to end-to-end coding [9].

With the mentioned advantages of RLNC, this technique has fitted well into many systems and applications. For example, in [10] RLNC is proposed and studied as a rateless FEC tech-nique for reliable satellite and also underwater acoustic communications, in [11] it is used as an alternative to hybrid ARQ for reliable data transmission in WiMAX unicast and in [12], it is utilized as an application level FEC technique to improve the performance of point-to-multipoint transmission of layered multimedia services. However, despite these and many other studies [13–21] that have investigated different aspects of RLNC, new challenges are still emerging in the field due to the constant demand for better quality of services and the consequent technology growth.

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§1.2 Thesis Contributions 3

RLNC and investigate the role of feedback.

1.2

Thesis Contributions

The contributions of this thesis are focused around the design and performance optimization of wireless RLNC and can be broadly discussed under two headings. The first one is RLNC for applications over TDD channels and the second one is RLNC for layered video streaming. More specifically, we make the following contributions:

• We study RLNC for reliable communication over half-duplex channels with memory and show the advantage of considering memory in minimizing the completion time [22]. • We study RLNC for delay sensitive applications over half-duplex channels and investi-gate the role of feedback through joint optimization of throughput and packet drop rate (PDR) [23, 24].

• We investigate RLNC for broadcasting of layered video and quantify the possible per-formance degradation caused by using feedback-free RLNC [25].

• We utilize RLNC for transmission of multiple layered streams and show the gain of coding across streams compared to coding only within streams [26].

In the next subsections, we describe each contribution in more detail.

1.2.1 RLNC for Applications over TDD Channels

The first class of problems we consider in this thesis is concerned with the use of RLNC for reliable communications over TDD channels with non-negligible RTTs, which is motivated by the studies by Lucani et. al. [9, 10, 27–30]. Such settings in [10] are referred to asdelay challenged environmentsand to emphasize the fact that the sender and receiver do not use the half-duplex channel in any predetermined fashion, they used the more general term of TDD channels, which we also use throughout this thesis.

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4 Introduction

aim at optimizing the feedback interval (rate) in a RLNC scheme, so that the expected time to complete the transmission of a block of packets, i.e.,completion time, can be minimized. This is also referred to as the delay in block transmission in [27].

In this thesis, we build upon these studies and investigate two unaddressed RLNC problems for such delay challenged environments: i) communication over erasure channels with memory and ii) transmission of delay sensitive applications.

1.2.1.1 RLNC for TDD Erasure Channels with Memory

A common approach to deal with the channel erasures is to consider erasures that occur inde-pendently across time slots, which makes the erasure channel model a memoryless one. While this assumption is valid in some situations, in many wireless applications, where deep fades in the channel cause temporally correlated bursty erasures, the memoryless models may not be applicable or efficient.

Therefore, we focus on transmission of blocks of packets over TDD channels withmemory

using RLNC. We consider a single-user scenario and our aim is to obtain insight into the impact of channel memory on RLNC design and performance optimization, which is unknown even for this simple case.

To this end, we propose a more general framework for optimization of RLNC comple-tion time compared to [27], by making use of bit-level and packet-level Gilbert-Elliot channel (GEC) [31, 32]. Our framework contains, as a special case, the memoryless TDD erasure channel studied in [27] and enables incorporating erasure memory into our RLNC transmis-sion design. Hence, we investigate the combined effect of erasure memory and rate, as well as packet length, feedback rate and RLNC parameters on the completion time performance, and consequently throughput performance of RLNC.

Through numerical examples, we show that by taking channel memory into account in transmission decisions, we can improve the completion time by as high as 74% when the erasure memory and erasure rates are high.

1.2.1.2 RLNC for Delay Sensitive Applications over TDD Channels

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com-§1.2 Thesis Contributions 5

pletion time, in order to study RLNC for delay sensitive applications over TDD channels. In such settings, since the sender has limited time to deliver all the packets of a block to the receivers, it should smartly dedicate the available time to transmission of RLNC packets and reception of feedback. Therefore, to design optimum RLNC-based transmission schemes for delay sensitive applications over TDD channels, in addition to the feedback rate and the RLNC parameters, we take into account the maximum possible number of feedback rounds as well.

Here, we consider the throughput and packet drop rate (PDR) as the performance metrics and our purpose is to investigate their joint optimization within the delay requirements of the application and the imposed physical limitations of the channel such as RTT. To this end, we start with a single-user case and formulate the performance metrics to investigate the advantage of using feedback. We compare the performances of feedback-free and feedback schemes and analytically show that the feedback-free scheme outperforms the feedback scheme when RTT is large. That is, in large RTT settings, it is better to dedicate all the time to information transmission rather than waiting a long time for feedback. Then we extend our analysis to multi-user broadcast case, where we consider a number of different broadcast scenarios and optimize the system parameters to achieve the best overall performance.

Furthermore, we study the complicated trade-off between the throughput and PDR. That is, for reducing PDR more RLNC packets of the same block should be sent so that each receiver is more likely to decode before the deadline. However, this increases completion time and consequently, results in lower throughput. So the optimum solution is not trivial, especially when multiple users have different PDR and throughput requirements or experience different packet erasure conditions. Then, to better analyze the throughput performance of the proposed feedback-free scheme, we formulate the probability and cumulative density functions (PDF and CDF) of users’ throughputs and utilize them to investigate the problem of guaranteeing a certain quality of service (QoS).

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6 Introduction

1.2.2 RLNC for Layered Video Streaming

The second class of problems we consider in this thesis is concerned with the use of RLNC for transmission of layered video streams over wireless networks. In video streaming, timely delivery of high quality content is desirable, but this is often hindered by delay, packet loss and bandwidth limitations. These challenges are even more restrictive when video is trans-mitted over wireless networks. To deal with these challenges, a number of useful features has been added to video streaming standards. For instance, the scalable video coding (SVC) of H.264 [33] provides layered video streams with various levels of quality, which can be useful when there is heterogeneity in users’ reception capabilities or displays.

The layered approach can be even more beneficial when combined with FEC techniques [34], as it provides unequal error protection (UEP) for different importance layers and the quality of video streaming can be further improved. Such combinations are studied in [35, 36] for Reed-Solomon and Fountain codes, respectively.

In this thesis, we consider the combination of RLNC and UEP, which will be referred to as ‘UEP+RLNC’, and investigate some open problems in: i) broadcasting of layered video and ii) transmission of multiple layered video streams.

1.2.2.1 RLNC for Broadcasting of Layered Video

The authors in [37] investigated the problem of streaming layered video in content delivery and P2P networks. They combined RLNC and random push-based streaming and proposed a hier-archical RLNC framework to better protect more important video layers. Later, Vukobratovic et. al. in [38] proposed to combine UEP with feedback-free RLNC to achieve an improved performance over non-NC schemes for single user settings. They investigated the method of coding across layers (i.e., inter-layer coding), as one step forward compared to coding only within layers (i.e., intra-layer coding) and showed the gain of inter-layer UEP+RLNC over intra-layer UEP+RLNC. This approach was then used in [39] for sliced video streaming and adapted to 3GPP Long Term Evolution-Advanced (LTE-A) standard in [12].

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§1.2 Thesis Contributions 7

comparing feedback-free schemes with an idealistic full-feedback schemes.

To this end, we study ‘expected ratio of decoded frames’ as a key content-independent per-formance metric and propose a novel framework for calculation of this metric. The framework we propose for obtaining this theoretical performance metric is general and can be calculated for different video and system parameters, e.g., packet error rate (PER), number of packets per layer, number of layers and number of possible transmissions. In addition to studying the effect of different parameters, we study the effect of number of video layers and propose a scheme that selects the optimum number of layers adaptively to achieve the highest performance.

To put our results into perspective and compare with full-feedback scheme as an upper-bound, we study an idealistic inter-layer UEP+RLNC scheme, where perfect, i.e. lossless and instantaneous, feedback about users’ reception status is assumed to be available at the sender after every transmission. We utilize the finite horizon MDP [40] to obtain the optimal performance of this idealistic scheme and then compare it with our proposed feedback-free scheme.

We assess the performance of the designed optimal schemes via real H.264/SVC encoded video test streams and consider various systems parameters. We discuss the trade-offs among the users’ performances and show the gain of adaptive selection of number of layers to improve the trade-offs. Furthermore, it will be observed that the performance gap between the proposed feedback-free scheme and the idealistic scheme is small and the adaptive selection of number of video layers further closes the gap.

1.2.2.2 RLNC for Transmitting Multiple Layered Video Streams

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8 Introduction

but degrades as network becomes more heterogeneous.

1.3

Thesis Outline

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Chapter 2

Background and Related Work

2.1

Network Coding

Network coding (NC) is a technique emerged at the start of this millennium in the seminal paper by Ahlswede et. al. [4]. Since then, NC has gained much attention and popularity in different areas of wired and wireless communications and numerous works have investigated and developed both the theoretical and practical aspects of this technique. Network coding, in a simple and concise expression, is mixing or encoding of messages inside a network such that the messages can be unmixed or decoded at their final destinations [41]. To illustrate the basic concepts of NC and expected benefits, let us consider the following well-known example in the NC literature.

Example 2.1. Consider the butterfly network, depicted in Fig. 2.1. The source wants to trans-mit a two-bit message to both receivers R1 and R2. Assume we have slotted time and each transmission can carry one bit. In a traditional routing scenario, after V has received botha andbbits, it sends them one after another in two transmissions. In a scenario using NC, as discussed in [42], V can send a combination ofaandb(i.e., encode them asab, where⊕ denotes the XOR operation) in one transmission; then both bits can be obtained (i.e., decoded) by both R1 and R2 after total of 9 transmissions, which is at least one transmission less com-pared to the traditional routing scenario. Hence, it can be concluded that using NC leads to lower transmission time and higher throughput [42].

In the example above, a simple case ofmulticasting, which is the transmission of messages from a source node to a subset of nodes in a network, is considered. It is now well known that to transmit messages over a generic network, systems using NC can exploit the available re-sources (e.g., bandwidth and energy) more efficiently compared to the traditional systems using only simple routing and scheduling methods. In fact, NC is capable of improving bandwidth

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10 Background and Related Work

Source

T U

V

W

R1 R2

a b

a b

[image:34.595.207.349.113.286.2]

a ? b

Figure 2.1: The butterfly network. A message is represented by two bitsaandband the source wants to multicast the message to receivers R1 and R2. In a scenario using NC, V transmits a

combination of bits, i.e.,ab.

utilization and loss resilience, as well as reducing transmission time and energy.

2.1.1 Fundamental Studies

Network coding was initially proposed in the seminal paper by Ahlswede et. al. [4]. In this work, a communication network was considered in which a number of information sources were to be multicast to certain sets of destinations and the problem of characterizing the ad-missible coding rate region was studied. It was shown that by allowing nodes in the network to process their incoming information streams, instead of just forwarding them, the bandwidth can in general be saved. Moreover, it was concluded that this encoding at the nodes, which is referred to as network coding, is necessary and sufficient to achieve the multicast capacity of a general network.

This study was later extended with the introduction of linear NC by Li et. al. [43] and algebraic NC by Koetter and Médard [44]. Linear NC means that messages can be considered as vectors of elements from a finite field of sizeq, which is denoted byFq, and the encoding functions at the nodes can be simple linear combinations over this finite field. In fact, XOR-ing the bits in Example 2.1 is a linear NC overF2. Both studies in [43, 44] considered the

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§2.1 Network Coding 11

of multicast connection; [44] proposed an algebraic framework for general NC that extended previous results to arbitrary networks and considered robust networking as well.

Later, Chou et. al. [13] took into account various practical considerations and proposed a

distributedscheme for practical NC that, in contrary to previous studies, obviates the need for centralized knowledge of network topology and also encoding and decoding functions. More-over, they introducedgenerationsbased NC, where each generation contains a fixed number of packets and only packets inside one generation are encoded together. The proposed scheme was shown to be robust to random packet loss and delay as well as robust to changes in the network topology or capacity.

Fragouli et. al. [45] were among the first to consider the use offeedbackfor NC. They illus-trated, through a number of case studies, that use of feedback can be beneficial for parameter adaptation to satisfy quality of service (QoS) requirements as well as for reliability purposes and also reduction of resources, such as memory elements and bandwidth consumption. They discussed that, instead of acknowledging each received packet from a generation, receivers can feed back the information about the number of independent packets required to decode the whole generation. This is referred to as acknowledging degrees of freedom (DOF) and will be later discussed in Chapter 3.

Based on whether feedback (also referred to as acknowledgments or reception reports) are used for NC code construction or not, we can broadly categorize NC methods into two groups: i) no-feedback NC and ii) feedback-based NC. In the latter category, more intelligent coding choices can be made by allowing nodes to share their knowledge with other nodes via using feedback. The benefits and drawbacks of using feedback for code construction is later discussed in Section 2.2. As an important example from the first category, we can refer to

random linear network coding (RLNC), which will be the main focus in this thesis and will be described further in the next subsection and also in the next chapter. As important examples of feedback-based NC, we can refer to opportunistic NC [46], online NC [47–50] and instantly decodable NC (IDNC) [51–55].

2.1.2 Random Linear Network Coding

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12 Background and Related Work

These mappings were selected independently at each node and the receivers only needed to know the overall linear combination of source packets in each of their incoming transmissions. It was shown that this approach achieves the multicast capacity with probability exponentially approaching 1 with the code length1. Furthermore, a bound on the required field size was obtained.

Lun [56] extended the above RLNC study and investigated the use of distributed RLNC in lossy packet networks. It was shown that by allowing the side-information in packet headers to grow arbitrarily large, the RLNC framework can achieve packet-level capacity for both single unicast and single multicast connections and for models of both wireline and wireless networks. The studies in [3, 13, 56] in fact laid the foundations for RLNC, which is now a major branch of NC research and the basis for many practical applications of NC.

As an important practical example of RLNC, we can refer to the study in [57], where the authors proposed MORE (which stands for MAC-independent Opportunistic Routing and Encoding) to study both unicast and multicast over wireless mesh networks. Here, the inter-mediate nodes, instead of just forwarding the packets, randomly mix packets together, before passing them to other nodes. This randomness ensures that routers that hear the same trans-mission do not forward the same packets. The proposed MORE was implemented between the IP and MAC layers and it was shown that throughput gain of between22−45%for unicast scenarios and35−200%for multicast scenarios over conventional methods can be achieved.

RLNC has since been used for various application and its gain and performance have been investigated under various settings [9, 11, 12, 14, 16–20, 27–30, 37–39, 58–67], which will be later reviewed in this chapter.

2.1.3 Applications of Network Coding

Followed by the above mentioned fundamental studies on NC, research on NC was then ex-tended into different areas [63, 68–74]. In these studies NC is investigated for large scale content distribution [68], ad hoc multicast [69], two-way wireless relaying [70], cooperative diversity [71], live peer-to-peer streaming [63], wireless broadcast [72,73] and distributed stor-age systems [74]. Comprehensive reviews on NC fundamentals, theory and applications are available in [41, 42, 75–80] that can be used for further reading.

As indicated in Chapter 1, we utilize RLNC for wireless broadcast in this thesis and most

1

Code length is the logarithm of the field size,C=log2q, and is also referred as the symbol size. This is later

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§2.2 Practical Issues in Implementation of Network Coding 13

of our research focuses on delay sensitive applications.

2.2

Practical Issues in Implementation of Network Coding

In many of the fundamental studies discussed above, it is well researched that NC can utilize the available bandwidth efficiently for transmission of messages. Let us define the throughput for a user as the ratio of the number of messages to the number of transmissions required to deliver all the messages. Then it is well known that NC can improve the average throughput in a network.

However, this theoretical throughput gain of NC comes with some implementation chal-lenges and practical considerations [13, 79, 81], based on the selected field size and generation size and also use of feedback that we now discuss.

The first important issue is concerned with the selected field size q, which can affect the complexity of NC operations as well as the performance of NC. Considering the RLNC method discussed previously, the multicast capacity can be asymptotically achieved only if the selected field sizeqis sufficiently large [3]. However, the field size cannot be selected arbitrarily large as it leads to complex encoding and decoding operations. Hence, a trade-off between the complexity of operations and the performance of NC, which is caused by the choice of q, should be considered in practice.

Another important issue is concerned with the selected generation size, which is the num-ber of messages encoded together. The generation size, similar to the field size, affects both the complexity of operations and the performance of NC [82]. Considering linear NC, the decod-ing at each node requires solvdecod-ing a set of linear equations, which is commonly done through using Gaussian elimination [13]. If we consider that the generation size isM, the complexity of decoding using Gaussian elimination is O(M3). Therefore, while choosing large genera-tion sizes could be beneficial in improving the throughput performance of NC [79], it may not be feasible in practice due to the increased decoding complexity.

The selected generation size, in addition to affecting the complexity of decoding operations and the throughput performance of NC, also affects thedelayperformance of NC as we now explain. Assuming RLNC with the generation size ofM, the receiving nodes require to receive at leastM encoded messages before being able to perform the decoding2. Therefore, ifM is chosen large to increase the throughput gain of NC, it can cause a large delay in delivering the

2

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14 Background and Related Work

messages to the nodes. In [10], this is explained as the possibility of having good throughput by delivering one truck with large storage once a year, which is not always desirable. Let us further explain this through the following example.

Example 2.2. Consider a simple system consisting of a sender and a receiver. We assume the generation size is M and the sender is supposed to deliver theseM packets by transmitting Ns = αM RLNC coded packets. As will be explained in Chapter 4 (in particular via (4.1) and (4.5)), an upper-bound for the probability of decoding all the packets in a generation, which is also reflective of mean throughput, can be obtained as

η= Ns

m=M (Ns

m)(1−Pe)

mPNsm

e (2.1)

where Pe is packet erasure probability for the channel between the sender and the receiver. Considering different values for M andα, the graphs in Fig. 2.2 are obtained. Suppose the sender wants to transmit a block of 40 packets to the receiver. In the first scenario, let us assume α = 1.1, which means the sender can transmit 44 RLNC packets in total. From the results in Fig. 2.2, it can be observed that choosing the generation size asM = 10results in the highest mean throughput. Hence, the sender transmits 11 RLNC packets for each batch of 10 packets. In another scenario, if we assume α = 1.2, it can be observed that choosing the generation size as M = 40 gives the highest mean throughput. However, in this case the receiver has to wait at least 40 time slots, before it can decode anything. As this may not be desirable in some applications, the sender may alleviate this large delay by choosing smaller generation sizes, e.g. transmitting 12 RLNC packets for each batch of 10 packets, but at the expense of degradation in mean throughput. This is known as the trade-off between the throughput and delay performances of RLNC, caused by the generation size.

We note that delay in the context of NC has various notions and definitions [83] and their discussion falls beyond the scope of this thesis. Here we mostly focus on one notion of delay which is the completion time of a generation as we shall explain in the next subsection.

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§2.2 Practical Issues in Implementation of Network Coding 15

1 1.1 1.2 1.3 1.4 1.5 0

0.2 0.4 0.6 0.8 1

α

η

M = 10

M = 20

M = 40

Figure 2.2: The probability of decoding all theM packets in a generation, whenNs = αM RLNC packets are transmitted. Packet erasure probability is assumed asPe=0.1.

encode messages intelligently, even some of the so-called “no-feedback” schemes cannot to-tally go without feedback. For example, in rateless RLNC, receivers need to inform the sender once the decoding of messages from current generation is finished. However, using feedback requires utilization of some of the available bandwidth, which can impact the NC throughput negatively and can also cause delay, specially if the round trip time of the channel is large and/or if the channel is not full duplex. Furthermore, it can lead to increased complexity of intelligent encoding at the sender for the feedback-based NC types.

To address these issues, different NC methods have been proposed over the past decade that have tried to investigate a subset of these issues under different system models. For instance, the XOR-based NC, which was initiated with the COPE architecture [46] and is also used in online NC [47–50] and instantly decodable NC [51–55], in fact tries to reduce the complexity of operations by using NC overF2. Another example is the use of systematicNC (e.g., [11,

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16 Background and Related Work

2.3

Delay Analysis of Network Coding

As some of the early works for investigating the delay performance of NC, we can refer to studies by Eryilmaz et. al. [14, 58]. In these studies, the authors investigated the delay gain of RLNC over scheduling methods for file transmission over unreliable single-hop wireless networks. The delay was defined as the time to transmit the file to all interested receivers completely and it is also referred to as completion time in the literature and this thesis. They assumed the field sizeqto be sufficiently large and obtained the analytical formulation of the mean completion time for two distinct cases, with and without channel side information (CSI). In the former, real-time channel status was known at the sender by assuming availability of perfect feedback but in the latter, only channel statistics were known at the sender and receivers were asked to send a single ACK only after receiving the whole file. Using the obtained analytical expressions for the mean completion time, it was shown that the mean completion time achieved by RLNC is much shorter compared to uncoded scheduling methods.

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§2.3 Delay Analysis of Network Coding 17

coded packets to be sent before stopping for feedback. Their numerical results showed that the proposed scheme outperforms optimal non-NC scheduling policies in terms of the mean completion time.

In [14, 17, 27, 28, 58, 59] discussed above, it was assumed that the field size is sufficiently large, so that coded packets can be considered linearly independent with high probability. How-ever, for a more accurate system model, Lucani et. al. studied in [29] the actual effect of field size on the decoding probabilities. They showed through numerical results that if RLNC over field size of 2 is optimized, the degradation in the mean completion time performance is not so large. Finally, in [30], they investigated the performance of systematic NC for TDD channels. Their results showed that systematic RLNC overF2can provide completion time performance

very similar to that of RLNC scheme that uses very large field sizes, with the added advantage of requiring fewer and simpler operations during the decoding process. Similar observations on the sufficiency of systematic RLNC over F2 for implementation in mobile devices was

reported in [60].

The studies on NC delay analysis discussed so far were mostly focused on the mean (av-erage) delay. Nistor et. al. in [18, 61] investigated the distribution of delay for RLNC. Their works were motivated by applications with deadline, where considering the average delay may not be sufficient in guaranteeing delivery before a specific deadline. In their studies, feedback is limited to one acknowledgment for the reception of all symbols. They formulated the distri-bution of delay for the single-receiver case in [61] and extended their work to the two-receiver case in [18]. Comparisons with ARQ with perfect feedback, round robin scheduling, and LT codes [5] revealed that RLNC with q = 16 offers the best delay performance. Moreover, it was shown that usingq =2leads to a delay distribution with a heavy tail, which implies that XOR-based RLNC although simple to implement bears a cost in terms of worst-case delay.

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18 Background and Related Work

2.4

Network Coding for Delay Sensitive Applications

Analysis of NC delay in many of the studies discussed in Section 2.2 has been motivated by delay sensitive applications with strict delivery deadline. In this section, we review some of the most relevant NC studies that incorporated the delivery deadline constraints into the design of NC schemes.

As the first example of such studies, we can refer to the work by Yazdi et. al. [11] that investigated delay sensitive WiMAX unicast applications using MAC layer RLNC. To avoid the problem of ACK packet overhead found in Hybrid ARQ (HARQ), they considered only one ACK packet per each block ofM data packets. The objective was to find the optimum RLNC schemes that achieve the lowest packet drop rate (PDR), which is the loss probability of original packets by the deadline. They proved that MAC layer systematic NC (MSNC), which transmits the packets uncoded once and employs RLNC for retransmissions, achieves the optimum performance in terms of the PDR.

In [15, 16], Sorour and Valaee studied variations of RLNC for applications with delivery deadline over some geostationary satellite systems. Their aim was to improve the perfor-mance of ARQ. In conventional ARQ (i.e., Selective-Repeat, SR-ARQ), the original packets are sent uncoded, and then based on the negative ACKs, retransmissions are sent. Since the SR-ARQ needs to wait a full RTT before the retransmission of undelivered packets, the au-thors in [15] proposed a NC-ARQ algorithm that benefits from this waiting period to transmit random combinations of previously undelivered packets. The simulation results revealed that their algorithm achieves lower average packet delay, as well as lower PDR in comparison to SR-ARQ.

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§2.5 Network Coding for Video Streaming 19

NC scheme has higher average throughput compared to SR-ARQ and even NC-ARQ.

The works by Yang et. al. [19, 84] later studied adaptive NC for scheduling real-time traffic with hard deadlines over a single-hop wireless network. In their adaptive technique, the sender sequentially adjusts the generation size of RLNC to achieve the best performance in terms of the maximum throughput. To this end, they assumed the sender has the immediate information about the reception status of users (via perfect feedback). Hence, this information was taken into account together with the remaining time to the deadline to model the rate adaptation problem as a finite-horizon MDP. In addition to analytical and simulation results, they implemented the adaptive NC schemes in a realistic wireless emulation environment and demonstrated the feasibility of the proposed techniques in real time.

The authors in [20] investigated joint coding and scheduling optimization in wireless sys-tems withvaryingdelay sensitivities. They utilized RLNC with single feedback, which is to acknowledge the complete transmission of a generation, and investigated the trade-offs be-tween throughput and per-packet delay in single-hop wireless networks. To this end, they considered delays associated with transmission of data packets and also feedback and defined a general class of delay metrics based on the norms of packet arrival times. This general definition of delay enables capturing the delay sensitivities across different types of network applications. Hence, the optimal trade-off between throughput and per-packet delay for the single-user case was studied. Then, they extended the problem to broadcasting to multiple receivers having different delay constraints and feedback delays and formulated the problem as a generalized geometric program (GGP). The results showed that their approach allows the transmitter to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints.

2.5

Network Coding for Video Streaming

An important example of delay-sensitive applications for which NC has shown to be promising is multimedia streaming. There are diverse and abundant studies in this area as described in the review paper [85]. In this section, we chronologically review some of the works on NC for multimedia streaming that are most relevant to this thesis.

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20 Background and Related Work

of RLNC. Using the push based RLNC, it was shown that this technique improves the playback performance and also reduces the required overhead for exchanging side information between peers.

Later, Seferoglu and Markopoulou in [86] investigated video-aware opportunistic XOR-based NC over wireless networks. In this study the key insight was that when packets to be mixed are from video streams, network codes should be selected so as to maximize not only the network throughput but also the video quality. Therefore in their proposed scheme, the importance of video packets was first determined based on the deadline and contribution to the video quality. Then, considering the decodability of packets by several users, efficient network codes to maximize the overall video quality were selected. Through assessing the proposed scheme for different network topologies under different channel conditions and different de-lay budgets, significant gain of the proposed video-aware opportunistic NC over scheduling algorithms without NC was shown.

Gheorghiu et. al. in [64] investigated the problem of multi-resolution wireless video stream-ing to a heterogeneous set of receivers with different subscription levels usstream-ing RLNC. They proposed a layered RLNC approach that prioritized packets of more important layers. They considered minimal feedback, which means each user sends a positive feedback only when it can decode the desired level of quality. They simulated the system using synthetic constant bit rate video traffics with both realistic and perfect feedback and showed that the layered RLNC scheme outperforms both standard RLNC and non-NC schemes. In [65], the authors consid-ered the same system model and studied the problem of security in transmission of wireless video. They demonstrated that by exploiting the algebraic characteristics of RLNC, in addition to hierarchical fidelity levels and robustness against wireless packet loss, efficient security can also be achieved.

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§2.5 Network Coding for Video Streaming 21

RLNC and uncoded schemes and demonstrated the gain in saving bandwidth and reducing per-layer transmission delay.

Similar to [86], the authors in [87] also considered quality and deadline of video packets and studied NC-based scheduling for media transmission to multiple users over a WiMAX-like network. They considered layered video streams and proposed to employ the finite horizon MDP to select efficient network codes for transmissions of media packets with varying impor-tance. Based on this, they proposed a simulation-based dynamic programming algorithm that has a much lower run time compared to the conventional dynamic programming techniques, yet empirically converges quickly to the optimal solution. Their scheme showed to outperform non-NC schemes in multiuser single-hop wireless networks for both broadcast and multiple unicasts scenarios.

The study in [66] considered P2P layered video streaming over lossy overlay networks. The authors proposed to exploit network path diversity via a novel RLNC approach that pro-vides unequal error protection (UEP) to the packets conveying the video content. They de-signed a distributed receiver-driven streaming solution, where a client requests packets from different layers from its neighbors in the overlay. Based on the received requests, a node in turn forwards combinations of the selected packets to the requesting peers. Choosing a net-work coding strategy at every node was modeled as an optimization problem that determines the rate allocation between the different layers such that the average distortion at the requesting peer is minimized. It was demonstrated through simulation results that the proposed solution outperforms baseline NC strategies for P2P delivery of scalable video content.

In [38] Vukobratovic and Stankovic considered transmission of layered multimedia for uni-cast through packet erasure channels without feedback. Similar to [37, 64, 66] and to place a better protection on the more important packets of the source message, the authors investigated the combination of RLNC and UEP. However, in contrast to previous studies that demonstrated the merit of such techniques through simulation results, this study contributed to the theoret-ical understanding of the design and performance of the UEP+RLNC schemes. They derived theoretical performance for packet-level UEP coding, which encodes packets of each impor-tance class independently (non-overlapping windowing strategy, NOW) or jointly (expanding windowing strategy, EW). Then, they demonstrated that the general performance limits of both strategies are achievable by probabilistic encoding over non-overlapping and expanding win-dows based on RLNC.

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22 Background and Related Work

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Chapter 3

Random Linear Network Coding for

Time Division Duplexing Channels

3.1

Chapter Goals

This chapter consists of two main parts. In the first part, random linear network coding (RLNC), as the main technique to be studied and utilized in this thesis, is introduced in Sec-tion 3.2. We start by discussing the general model for RLNC encoding and decoding and present common RLNC notations and definitions. Then, we consider RLNC for applications over time division duplexing (TDD) channels and discuss challenges for systems operating over large latency channels.

In the second part, we study RLNC for TDD channels with memory in Section 3.3, which is one contribution of this thesis. In this system, a sender transmits blocks ofM data packets to a single receiver and the objective is to study the impact of channel memory on the design and performance of RLNC.

3.2

Random Linear Network Coding

Random linear network coding is the basis of many practical applications of network coding today. Introduced in [3] for achieving the multicast capacity in lossless packet networks, this coding technique soon gained much attention and is now becoming off-the-shelf [88] for many systems and applications including content distribution and storage, multimedia streaming and broadcasting, and mobile and wireless communications [7, 8].

The popularity of RLNC lies in its superior characteristics compared to other methods used for scheduling and error control in data transmission over unreliable communication channels. As an example of desirable RLNC characteristics, it is well known that RLNC

Figure

Fig. 3.7, and also for π−T our schemememoryless schemeMPercentage of mean completion time reduction for two RTTs of
Figure 2.1: The butterfly network. A message is represented by two bits a and b and the sourcewants to multicast the message to receivers R1 and R2
Figure 3.5: Markov chain representation of the RLNC schemes with infrequent feedback. In(a), states show the rDOF, i.e
Figure 3.7: Mean completion time for transmission of M data packets in an erasure channelwith memory
+7

References

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