Allerton 2015 Paper Abstract

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Paper ThA3.2

Arbabjolfaei, Fatemeh (University of California, San Diego), Kim, Young-Han (UCSD)

Three Stories on a Two-Sided Coin: Index Coding, Locally Recoverable Distributed Storage, and Guessing Games on Graphs

Scheduled for presentation during the Regular Session "Data Storage" (ThA3), Thursday, October 1, 2015, 08:50−09:10, Butternut

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Data Storage, Network Coding

Abstract

Three science and engineering problems of recent interests---index coding, locally recoverable distributed storage, and guessing games on graphs---are discussed and the connection between their optimal solutions is elucidated. By generalizing recent results by Shanmugam and Dimakis and by Mazumdar on the complementarity between the optimal broadcast rate of an index coding problem on a directed graph and the normalized rate of a locally recoverable distributed storage problem on the same graph, it is shown that the capacity region and the optimal rate region of these problems are complementary. The main ingredients in establishing this result are the notion of confusion graph introduced by Alon et al. (2008), the vertex transitivity of a confusion graph, the characterization of the index coding capacity region via the fractional chromatic number of confusion graphs, and the characterization of the optimal rate region of the locally recoverable distributed storage via the independence number of confusion graphs. As the third facet of the complementarity, guessing games on graphs by Riis are discussed as special cases of the locally recoverable distributed storage problem, and it is shown that the winning probability of the optimal strategy for a guessing game and the ratio between the winning probabilities of the optimal strategy and a random guess can be characterized, respectively, by the capacity region for index coding and the optimal rate region for distributed storage.

 

 

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