NDLI: Duality Codes and the Integrality Gap Bound for Index Coding

Content Provider	IEEE Xplore Digital Library
Author	Hao Yu Neely, M.J.
Copyright Year	1963
Abstract	This paper considers a base station that delivers packets to multiple receivers through a sequence of coded transmissions. All receivers overhear the same transmissions. Each receiver may already have some of the packets as side information, and requests another subset of the packets. This problem is known as the index coding problem and can be represented by a bipartite digraph. An integer linear program is developed that provides a lower bound on the minimum number of transmissions required for any coding algorithm. Conversely, its linear programming relaxation is shown to provide an upper bound that is achievable by a simple form of vector linear coding. Thus, the information theoretic optimum is bounded by the integrality gap between the integer program and its linear relaxation. In the special case, when the digraph has a planar structure, the integrality gap is shown to be zero, so that exact optimality is achieved. Finally, for nonplanar problems, an enhanced integer program is constructed that provides a smaller integrality gap. The dual of this problem corresponds to a more sophisticated partial clique coding strategy that time-shares between maximum distance separable codes. This paper illuminates the relationship between index coding, duality, and integrality gaps between integer programs and their linear relaxations.
Sponsorship	IEEE Information Theory Society
Starting Page	7256
Ending Page	7268
Page Count	13
File Size	1991250
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Indexes Vectors Linear programming Unicast Linear codes IP networks integrality gap Index coding
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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