On achievability of linear source coding over finite rings

We propose using linear mappings over finite rings as encoders in the Slepian-Wolf and the source coding for computing problems. It is known that the arithmetic of many finite rings is substantially easier to implement than the one of finite fields. Hence, one of the advantages of using linear mappi...

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Bibliographic Details
Published in:Proceedings / IEEE International Symposium on Information Theory pp. 1984 - 1988
Main Authors: Sheng Huang, Skoglund, Mikael
Format: Conference Proceeding
Language:English
Published: IEEE 01.07.2013
Subjects:
Context
Decoding
Polynomials
Random variables
Source coding
ISSN:2157-8095
Online Access:Get full text
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Summary:We propose using linear mappings over finite rings as encoders in the Slepian-Wolf and the source coding for computing problems. It is known that the arithmetic of many finite rings is substantially easier to implement than the one of finite fields. Hence, one of the advantages of using linear mappings over rings, instead of its field counterparts, is reducing implementation complexity. More importantly, the ring version dominates the field version in terms of achieving strictly better coding rates with strictly smaller alphabet size in the source coding for computing problem [1]. This paper is dedicated to proving an achievability theorem of linear source coding over finite rings in the Slepian-Wolf problem. This result includes those given by Elias [2] and Csiszár [3] saying that linear coding over finite fields is optimal, i.e. achieves the Slepian-Wolf region. Although the optimality issue remains open, it has been verified in various scenarios including particularly many cases use non-field rings [1], [4].
ISSN:2157-8095
DOI:10.1109/ISIT.2013.6620573