Bounding the Optimal Rate of the ICSI and ICCSI Problems

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Title: Bounding the Optimal Rate of the ICSI and ICCSI Problems
Authors: Byrne, Eimear
Calderini, Marco
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Date: 27-Jun-2017
Abstract: In this work we study both the index coding with side information (ICSI) problem introduced by Birk and Kol in 1998 and the more general problem of index coding with coded side information (ICCSI), described by Shum et al. in 2012. We estimate the optimal rate of an instance of the index coding problem. In the ICSI problem case, we characterize those digraphs having min-rank one less than their order and we give an upper bound on the min-rank of a hypergraph whose incidence matrix can be associated with that of a 2-design. Security aspects are discussed in the particular case when the design is a projective plane. For the coded side information case, we extend the graph theoretic upper bounds given by Shanmugam et al. in 2014 on the optimal rate of index code.
Funding Details: European Commission Horizon 2020
Type of material: Journal Article
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM Journal on Discrete Mathematics
Volume: 31
Issue: 2
Start page: 1403
End page: 1427
Copyright (published version): 2017 Society for Industrial and Applied Mathematics
Keywords: Index codingNetwork codingCoded side-informationMin-rankBroadcast with side-informationLinear programming
DOI: 10.1137/16M107164X
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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