Error control systems for digital communication and storage
Error control systems for digital communication and storage
DCC '04 Proceedings of the Conference on Data Compression
A general and optimal framework to achieve the entire rate region for Slepian-Wolf coding
Signal Processing - Special section: Distributed source coding
Generalized Bezout's theorem and its applications in coding theory
IEEE Transactions on Information Theory
Distributed source coding using syndromes (DISCUS): design and construction
IEEE Transactions on Information Theory
On code design for the Slepian-Wolf problem and lossless multiterminal networks
IEEE Transactions on Information Theory
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We consider the problem of compression of multiple correlated sources. It is assumed that the sources are given as a sequence with neighbouring sources correlated in terms of Hamming distance. In previous work we derived a general Distributed Source Coding (DSC) framework that uses the parity check matrix of a suitably chosen block code C1. In this paper we focus on the special case that C1 is a cyclic code. This allows us to formulate our DSC framework in terms of polynomials. The polynomial structure has the advantage that it allows for implementation via efficient shift registers. We show that the Sylvester resultant of polynomials plays a crucial role in the DSC framework. We address the notion of "complementarity" of codes and specify the DSC framework in terms of the cyclic code C1 and the reciprocal C2 of its dual code for the special case that C2 is complementary to C1. We illustrate our polynomial DSC framework for a sequence of 3 sources through a (15, 7) BCH code C1 and the reciprocal of its dual code C2.