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On the achievable rates of sources having a group alphabet in a distributed source coding setting

Vinodh, K and Lalitha, V and Prakash, N and Kumar, PV and Pradhan, SS (2010) On the achievable rates of sources having a group alphabet in a distributed source coding setting. In: 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Sept. 29 2010-Oct. 1 2010 , Allerton, IL .

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We consider the problem of compression via homomorphic encoding of a source having a group alphabet. This is motivated by the problem of distributed function computation, where it is known that if one is only interested in computing a function of several sources, then one can at times improve upon the compression rate required by the Slepian-Wolf bound. The functions of interest are those which could be represented by the binary operation in the group. We first consider the case when the source alphabet is the cyclic Abelian group, Zpr. In this scenario, we show that the set of achievable rates provided by Krithivasan and Pradhan [1], is indeed the best possible. In addition to that, we provide a simpler proof of their achievability result. In the case of a general Abelian group, an improved achievable rate region is presented than what was obtained by Krithivasan and Pradhan. We then consider the case when the source alphabet is a non-Abelian group. We show that if all the source symbols have non-zero probability and the center of the group is trivial, then it is impossible to compress such a source if one employs a homomorphic encoder. Finally, we present certain non-homomorphic encoders, which also are suitable in the context of function computation over non-Abelian group sources and provide rate regions achieved by these encoders.

Item Type: Conference Paper
Publisher: IEEE
Additional Information: Copyright 2010 IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 20 Dec 2011 08:33
Last Modified: 20 Dec 2011 08:33
URI: http://eprints.iisc.ac.in/id/eprint/38959

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