List decoding of convolutional codes over integer residue rings

https://doi.org/10.1016/j.ffa.2021.101815Get rights and content
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Abstract

A convolutional code C over Zpr[D] is a Zpr[D]-submodule of Zprn[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 wC when some of its coefficients have been erased. We do that using the p-adic expansion of w and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field pr1Zpr. 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.

MSC

11T71
94B10
94B35

Keywords

Convolutional codes
Finite rings
Erasure channel

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