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

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Chapter 4: Unequal Erasure Protection (UEP) in Network Coding 35 last two layers depends on successful recovery of the third. Scalable data therefore asks for unequal erasure protection (UEP), sometimes mentioned as unequal loss protection (ULP), such that the parts of data with higher priority are better protected against erasures. m 5 m 5 m 4 m 3 m 2 m 1 m 4 m 3 m 2 m 1 m 2 m 1 Figure 4.1: Recovery of layered data with the third layer missing UEP has been implemented in several components of digital communication systems. UEP bit-loading for multi-carrier modulation was studied in [77], UEP coded modulation in [50], UEP bit-loading for MIMO-OFDM (Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing) in [37], UEP Turbo codes based on puncturing and pruning in [78], and UEP LDPC Codes based on irregular variable and/or check node degrees in [41, 68]. Unequal-erasure-protected network coding was proposed for the first time by us in [5]. We analyzed the effect of erasures on the recovery of scalable data when linear network coding was applied. We found that global encoding kernels (GEKs) describing linear network codes had different levels of built-in unequal-erasure-protecting (UEP) capability, allowing better protection of high-priority data when GEKs were wisely assigned. UEP in network coding is introduced in Section 4.3. We define some related economic terms and concepts of scalable data in Section 4.4, which allows us to give a mathematical expression of the expected utility of recovered scalable data in the presence of erasures in Section 4.5. In Section 4.6, we quantitatively show that linear network codes have built-in UEP mechanisms affecting the utility of the recovered scalable data. Section 4.7 discusses a UEP network code assignment problem, which will be simplified by a procedure described in Section 4.8 before being solved by two strategies suggested in Section 4.9 and 4.10. The last section discusses the results
36 Chapter 4: Unequal Erasure Protection (UEP) in Network Coding and concludes the topic. 4.2 The Edge-Disjoint Path Model with Binary Erasure Channels for Network Coding Figure 4.2 shows network coding in a network that is usually called the butterfly network, where A aims to multicast two binary symbols b 1 and b 2 to D and E. In Fig. 4.2, we can see that the node F encodes b 1 and b 2 together to achieve the multicast rate of 2 bits per unit time, if each edge represents the capacity of one bit per unit time, D receives b 1 from the path ABD and can recover b 2 from the symbol b 1 ⊕ b 2 from ACF GD, whereas E receives b 2 from the path ACE and recovers b 1 from the symbol b 1 ⊕ b 2 from ABF GD. Had network coding not been there, only either b 1 or b 2 would have been able to pass the bottleneck F G in one unit time, i.e., one receiver would have been unable to use one of its possible transmission paths [55]. A b 1 b 2 B C b 1 b 2 F b 1 b 1 ⊕ b 2 b 2 G b 1 ⊕ b 2 b 1 ⊕ b 2 D E Figure 4.2: Network coding in a butterfly network By means of network coding, all receivers can use all of their possible paths at the same time. In general, the multicast rate of ω suggests the existence of ω non-intersecting paths from the source to each sink, which are called edge-disjoint paths by Jaggi et al. [63],
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 10 and 11: List of Figures 2.1 A basic digital
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
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Page 72 and 73: Chapter 5: Network Coding with LT C
Page 88 and 89: Part III Wireless Physical-layer Se
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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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