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Chapter 4: Unequal Erasure Protection (UEP) in Network Coding 51 Table 4.2: The resulting expected utilities of the recovered scalable data in the network example when the suggested strategy is applied . E 3 [U 1 ] 1.4873 E 3 [U 2 ] 1.4873 E 3 [U 3 ] 1.4873 E 3 [U 4 ] 1.3973 min E 3 [U i ] 1.3973 a significant amount of quality can be saved if we take the UEP mechanism of network codes into consideration and apply the suggested strategy. Table 4.3: Comparison of minimum expected utilities of the received scalable data in the network example for different strategies . The Best The Suggested The Average over All The Worst Assignment Strategy Possible Assignments Assignment 1.3973 1.3973 1.3055 1.2757 4.10 An Ascending-bid Auction Algorithm for GEK Allocation Unlike the previous section, the objective of the GEK assignment algorithm in this section is a fair competition among sink nodes. We assume that the source node is an auctioneer and the sinks are participants who bid for the rights to choose GEK allocation. Since we will not give a monopoly to any single sink node, the allocation problem is formulated as a multiple-item auction. For this kind of auction, the dynamic counterpart of Vickrey’s effective static design [80] has been proposed since 2004 by Ausubel [39], whose idea will be used in our auction as follows. The source node calls a price, bidders respond with
52 Chapter 4: Unequal Erasure Protection (UEP) in Network Coding quantities, and the process iterates with increasing price until demand is not greater than supply. Although the supply is the total number of GEK allotments, it does not equal the total number of edges, because, as discussed earlier, some edges are forced by the topology to have the same GEK. Before the auction begins, the source node has to derive the minimum subtree graph of the network, as explained in Section 4.8 [3]. Let T represent the set of all subtrees. The source wishes to allocate |T | GEKs to |T | subtrees, not on its own but by means of a |T |-item auction. The sink i who wins x i items is allowed to choose the allocation of x i GEKs to x i subtrees in order to maximize its received utility. The source then distributes the data accordingly and informs the intermediate coding nodes about the local encoding functions they have to use [3]. According to Ausubel’s idea, a bidder’s payment is not the product of its final quantity and the final price. Rather, at the price ψ, the auctioneer sees if the aggregate demand x \i of bidder i’s competitiors is less than the supply |T |. If so, |T | − x \i items are clinched and awarded to the bidder i with the price ψ. Since the winner’s payment depends on its competitors bids and not its own bids, every participant has an incentive to reveal truthfully his or her value for the item. [39] Our auction, however, requires some modification since each clinched item and the resulting GEK allocation of a winning sink affects the demand of others. This is best explained by an example. Table 4.4: Preference order of GEK allocation . Sink Preference Order R 1 T 4 T 3 T 1 R 2 T 2 T 1 T 5 R 3 T 1 T 4 T 3 R 4 T 5 T 4 T 3 Suppose that the source node S in Fig. 4.4 would like to multicast an ordered scalable message M = [m 1 , m 2 , m 3 ], of which each element m i has a dependency level of i, to four sink nodes R 1 , R 2 , R 3 , and R 4 . We assume that Table 4.4 reflects the preference order
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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
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
Page 90 and 91: Chapter 6 Wireless Physical-layer S
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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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