Network Coding and Wireless Physical-layer ... - Jacobs University

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Chapter 5: Network Coding with LT Codes as Erasure Codes 73 algorithm and with Algorithm 5.1. We can see that Algorithm 5.1 reduces the variance of the number of required symbols, thus making the histogram of the latter case more concentrated near the middle at 1270. When both algorithms are applied, as shown in Fig. 5.10, the histogram resembles a left-shifted version of that in Fig. 5.9 when only Algorithm 5.1 is applied. Instead of simple histograms, Figure 5.11 plots normalized cumulative histograms to clearly show that less symbols are needed to be transmitted when both algorithms are applied. We can conclude that our cooperative scheme improves the receiving performance, not only when the erasure probability at BD is 0.1, but also when it is 0.2 and 0.05. The larger the erasure probability, the greater the improvement. In a more complicated network, a node can act as both a relay for upstream nodes and a source for downstream ones. Therefore, the subtree analysis as suggested in [14] is needed to identify whether a given node’s buffering scheme should follow Algorithm 5.1, Algorithm 5.2, or a modified algorithm combining both of them. In addition, the relationship between erasure probabilities in all edges and the suitable parameter p c used in Algorithm 5.2 should be studied further. In this work, the value of p c is 0.7492. 200 180 Without Algorithm 1 and 2 Only With Algorithm 1 160 140 Frequency 120 100 80 60 40 20 0 1000 1100 1200 1300 1400 1500 1600 Number of Symbols Needed to be Transmitted Figure 5.9: Comparison of histograms of the number of LT-encoded symbols needed to be transmitted in a coded butterfly network with the erasure probability of 0.1 at BD such that all original symbols are recovered in two cases, without using the proposed algorithm and with Algorithm 5.1
74 Chapter 5: Network Coding with LT Codes as Erasure Codes 200 180 Without Algorithm 1 and 2 With Algorithm 1 and 2 160 140 Frequency 120 100 80 60 40 20 0 1000 1100 1200 1300 1400 1500 1600 Number of Symbols Needed to be Transmitted Figure 5.10: Comparison of histograms of the number of LT-encoded symbols needed to be transmitted in a coded butterfly network with the erasure probability of 0.1 at BD such that all original symbols are recovered in two cases, without using the proposed algorithm and with Algorithms 5.1 and 5.2 1 0.9 0.8 normalized cumulative frequency 0.7 0.6 0.5 0.4 0.3 With Alg. 1 and 2, Erasure Prob. at BD=0.05 0.2 Without Alg. 1 and 2, Erasure Prob. at BD=0.05 With Alg. 1 and 2, Erasure Prob. at BD=0.1 0.1 Without Alg. 1 and 2, Erasure Prob. at BD=0.1 With Alg. 1 and 2, Erasure Prob. at BD=0.2 Without Alg. 1 and 2, Erasure Prob. at BD=0.2 0 1000 1100 1200 1300 1400 1500 1600 Number of Symbols Needed to be Transmitted Figure 5.11: Comparison of normalized cumulative histograms of the number of LTencoded symbols needed to be transmitted in a coded butterfly network with varying erasure probability at BD such that all original symbols are recovered in two cases, without using the proposed algorithm and with Algorithms 5.1 and 5.2
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Network Coding and Wireless Physica
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Abstract The general abstraction of
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Contents Abstract i Abstract ii Dec
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vi CONTENTS 5.4 Degree Distribution
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List of Figures 2.1 A basic digital
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x LIST OF FIGURES 5.11 Comparison o
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Part I Motivation, Overview, and In
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Chapter 1: Motivation and Overview
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Chapter 2 Introduction to Digital C
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Chapter 2: Introduction to Digital
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Chapter 3: Introduction to Graphs a
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Page 46 and 47: 33 The emergence of scalable video
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Page 132 and 133: Bibliography [1] 3GPP, “3GPP; Tec
Page 134 and 135: BIBLIOGRAPHY 121 [21] F.A. Hayek,
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BIBLIOGRAPHY 123 [43] M. Friedman a
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BIBLIOGRAPHY 125 [63] S. Jaggi, P.
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BIBLIOGRAPHY 127 [81] X. Sun, X. Wu
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Network Coding and Wireless Physical-layer ... - Jacobs University

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