Optimal Scalar Linear Index Codes for Some Two-Sender Unicast Index Coding Problems

Chinmayananda, A and Rajan, B Sundar (2019) Optimal Scalar Linear Index Codes for Some Two-Sender Unicast Index Coding Problems. In: Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, 28 - 31 October 2018, Grand Copthorne WaterfrontSingapore; Singapore, pp. 105-109.

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Abstract

In this paper, two-sender unicast index coding problem (TUICP) is studied, where the senders possibly have some messages in common, and each receiver requests a unique message. It is analyzed using three independent subproblems (which are single-sender unicast index coding problems (SUICPs)) and the interactions among them. These sub-problems are described by three disjoint vertex-induced subgraphs of the side-information graph of the TUICP respectively, based on the availability of messages at the senders. The TUICP is classified based on the type of interactions among the sub-problems. Optimal scalar linear index codes for a class of TUICP are obtained using those of the sub-problems. For two classes, we identify a sub-class for which scalar linear codes are obtained using the notion of joint extensions of SUICPs. An SUICP I-E is said to be a joint extension of l SUICPs if the fitting matrices of all the l SUICPs are disjoint submatrices of that of I-E. Joint extensions generalize the notion of rank-invariant extensions. Scalar linear codes and a condition for optimality of the codes are given for a class of joint extensions. Using this result, scalar linear codes and the conditions for their optimality are obtained for two classes of the TUICP.

Item Type:	Conference Proceedings
Series.:	15th International Symposium on Information Theory and Its Applications, ISITA 2018
Publisher:	IEEE
Additional Information:	15th International Symposium on Information Theory and its Applications (ISITA), Singapore, SINGAPORE, OCT 28-31, 2018
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering > Electrical Communication Engineering - Technical Reports
Date Deposited:	15 Jul 2019 07:01
Last Modified:	15 Jul 2019 07:01
URI:	http://eprints.iisc.ac.in/id/eprint/62907

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