Distributed source coding with cyclic codes and their duals

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.