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

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List of Figures 2.1 A basic digital communication system . . . . . . . . . . . . . . . . . . . . . 6 2.2 A secure digital communication system . . . . . . . . . . . . . . . . . . . . 6 2.3 Binary Erasure Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Binary Symmetric Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 (a) A network. (b) A spanning tree for the leftmost router. (c) A multicast tree of group 1. (d) A multicast tree of group 2 . . . . . . . . . . . . . . . 15 3.1 An example of a simple directed graph . . . . . . . . . . . . . . . . . . . . 18 3.2 An example of a multigraph . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Illustration of the max-flow problem as a special case of the minimum cost flow problem [17] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 (a) A graph G with the associated edge capacities, (b) the minimum cut of G, and (c) the maximum flow of G . . . . . . . . . . . . . . . . . . . . . 23 3.5 The butterfly network with edge capacities . . . . . . . . . . . . . . . . . . 24 3.6 Illustration of information flow within the butterfly network . . . . . . . . 25 3.7 Network coding in a butterfly network . . . . . . . . . . . . . . . . . . . . 26 3.8 The butterfly network with imaginary edges . . . . . . . . . . . . . . . . . 27 3.9 The butterfly network with global encoding kernels labelling all edges . . . 31 4.1 Recovery of layered data with the third layer missing . . . . . . . . . . . . 35 4.2 Network coding in a butterfly network . . . . . . . . . . . . . . . . . . . . 36 4.3 Another network coding pattern in a butterfly network . . . . . . . . . . . 38 viii
LIST OF FIGURES ix 4.4 Network example with scalable data multicast . . . . . . . . . . . . . . . . 47 4.5 Line graph derived from Fig. 4.4 . . . . . . . . . . . . . . . . . . . . . . . . 47 4.6 The minimum subtree graph derived from Fig. 4.5 . . . . . . . . . . . . . . 48 5.1 Network coding in a butterfly network . . . . . . . . . . . . . . . . . . . . 60 5.2 Detailed system model including LT-encoding and decoding blocks as well as the buffer structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3 Robust soliton distribution with k = 1000, c = 0.1, and δ = 0.5 . . . . . . . 63 5.4 Robust soliton distribution around the first peak in comparison with distorted distribution caused by erasures at the edge BD . . . . . . . . . . . 66 5.5 Robust soliton distribution around the second peak in comparison with distorted distribution caused by erasures at the edge BD . . . . . . . . . . 66 5.6 Histogram of the number of LT-encoded symbols needed to be transmitted in an erasure-free case such that all original symbols are recovered . . . . . 67 5.7 Comparison of histograms of the number of LT-encoded symbols needed to be transmitted such that all original symbols are recovered in two cases, a point-to-point communication with an erasure probability of 0.05 and a coded butterfly network with an erasure probability of 0.1 at BD . . . . . 67 5.8 Network coding in a butterfly network when only BD is erasure-prone . . . 68 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 . . . . . . . . . . . . 73 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 . . . . . . . 74
Page 1: Network Coding and Wireless Physica
Page 4 and 5: Abstract The general abstraction of
Page 6 and 7: Contents Abstract i Abstract ii Dec
Page 8 and 9: vi CONTENTS 5.4 Degree Distribution
Page 12 and 13: x LIST OF FIGURES 5.11 Comparison o
Page 14 and 15: Part I Motivation, Overview, and In
Page 16 and 17: Chapter 1: Motivation and Overview
Page 18 and 19: Chapter 2 Introduction to Digital C
Page 20 and 21: Chapter 2: Introduction to Digital
Page 30 and 31: Chapter 3: Introduction to Graphs a
Page 46 and 47: 33 The emergence of scalable video
Page 48 and 49: Chapter 4: Unequal Erasure Protecti
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Chapter 4: Unequal Erasure Protecti
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Chapter 5: Network Coding with LT C
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Part III Wireless Physical-layer Se
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Chapter 6 Wireless Physical-layer S
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Chapter 6: Wireless Physical-layer
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Chapter 7 Physical-layer Key Encodi
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Chapter 7: Physical-layer Key Encod
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Chapter 8: Summary, Conclusion, and
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Bibliography [1] 3GPP, “3GPP; Tec
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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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