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A Relation Between Network Computation and Functional Index Coding Problems

Gupta, Anindya and Rajan, Sundar B (2016) A Relation Between Network Computation and Functional Index Coding Problems. In: IEEE Information Theory Workshop (ITW), SEP 11-14, 2016, Cambridge, ENGLAND.

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Official URL: http://dx.doi.org/10.1109/ITW.2016.7606784

Abstract

In contrast to the network coding problem wherein the sinks in a network demand subsets of the source messages, in a network computation problem the sinks demand functions of the source messages. Similarly, in the functional index coding problem, the side information and demands of the clients include disjoint sets of functions of the information messages held by the transmitter instead of disjoint subsets of the messages, as is the case in the conventional index coding problem. It is known that any network coding problem can be transformed into an index coding problem and vice versa. In this work, we establish a similar relationship between network computation problems and a class of functional index coding problems, viz., those in which only the demands of the clients include functions of messages. We show that any network computation problem can be converted into a functional index coding problem wherein some clients demand functions of messages and vice versa. We prove that a solution for a network computation problem exists if and only if a functional index code (of a specific length determined by the network computation problem) for a suitably constructed functional index coding problem exists. Next we show that a functional index coding problem admits a solution of a specified length if and only if a suitably constructed network computation problem admits a solution.

Item Type: Conference Proceedings
Additional Information: Copy right for this article belongs to the IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Depositing User: Id for Latest eprints
Date Deposited: 07 Dec 2016 05:20
Last Modified: 07 Dec 2016 05:20
URI: http://eprints.iisc.ac.in/id/eprint/55494

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