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On the Broadcast Rate and Fractional Clique Cover of Single Unicast Index Coding Problems

Vaddi, Mahesh Babu and Rajan, B Sundar (2019) On the Broadcast Rate and Fractional Clique Cover of Single Unicast Index Coding Problems. In: 2018 IEEE Information Theory Workshop, ITW 2018, 25-29 Nov.,2018, Sun Yat-Sen Kaifeng HotelGuangzhou; China, pp. 160-164.

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Official URL: https://dx.doi.org/10.1109/ITW.2018.8613453

Abstract

The broadcast rate beta of an index coding problem is the minimum number of index code symbols required to transmit to satisfy the demands of all the receivers. The linear broadcast rate beta((l)) of an index coding problem is the minimum number of index code symbols obtained by linear encoding by using a encoding matrix. Blasiak et al. defined the fractional clique cover number of an undirected graph and used it to bound the broadcast rate of an index coding problem. Lubetzky et al. proved that nonlinear codes can outperform linear codes. In this paper, we find the fractional clique cover number of two classes of symmetric index coding problems. For single unicast index coding problems with symmetric consecutive and neighboring side-information, we prove that broadcast rate is equal to the fractional clique cover number. We define m-dimensional vector index code of an index coding problem by using disjunctive product of side-information graph. We prove that if linear broadcast rate is equal to fractional clique cover number, then, linear broadcast rate is equal to broadcast rate.

Item Type: Conference Paper
Additional Information: IEEE Information Theory Workshop (ITW), Guangzhou, PEOPLES R CHINA, NOV 25-29, 2018
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: R.S. Ranganayaki
Date Deposited: 25 Jun 2019 17:36
Last Modified: 25 Jun 2019 17:36
URI: http://eprints.iisc.ac.in/id/eprint/62825

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