List decoding of convolutional codes over integer residue rings

Abstract

A convolutional code Cover Zpr[D]is a Zpr[D]-submodule of Znpr[D]where Zpr[D] stands for the ring of polynomials with coefficients in Zpr. In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword w∈Cwhen some of its coefficients have been erased. We do that using the p-adic expansion of wand particular representations of the parity-check polynomial matrix of the code. Fr o m these matrix polynomial representations we recursively select certain equations that wmust satisfy and have only coefficients in the field pr−1Zpr. We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w.