On Syndrome Decoding for Slepian-Wolf Coding Based on Convolutional and Turbo Codes

TL;DR

This paper demonstrates that various convolutional and turbo syndrome decoding algorithms for Slepian-Wolf coding are equivalent and proposes an iterative message-passing implementation that leverages existing channel decoding structures.

Contribution

It formally proves the equivalence of different syndrome decoding algorithms and introduces a unified iterative decoding approach using message-passing techniques.

Findings

Different algorithms lead to the same estimate.

An iterative message-passing implementation is effective.

Utilizes existing channel decoding structures.

Abstract

In source coding, either with or without side information at the decoder, the ultimate performance can be achieved by means of random binning. Structured binning into cosets of performing channel codes has been successfully employed in practical applications. In this letter it is formally shown that various convolutional- and turbo-syndrome decoding algorithms proposed in literature lead in fact to the same estimate. An equivalent implementation is also delineated by directly tackling syndrome decoding as a maximum a posteriori probability problem and solving it by means of iterative message-passing. This solution takes advantage of the exact same structures and algorithms used by the conventional channel decoder for the code according to which the syndrome is formed.