Algebraic codes for Slepian-Wolf code design

TL;DR

This paper explores the use of Reed-Solomon codes for lossless distributed source coding in the Slepian-Wolf problem, demonstrating their robustness, rate adaptivity, and superior performance over LDPC codes in certain scenarios.

Contribution

It introduces algebraic soft-decision decoding of RS codes for the Slepian-Wolf problem, showing their advantages over LDPC codes in various correlation models and uncertain distributions.

Findings

RS codes outperform LDPC codes under q-ary symmetric correlation.

RS codes are more robust to inaccuracies in source distribution.

RS codes offer natural rate adaptivity and consistent performance across correlation structures.

Abstract

Practical constructions of lossless distributed source codes (for the Slepian-Wolf problem) have been the subject of much investigation in the past decade. In particular, near-capacity achieving code designs based on LDPC codes have been presented for the case of two binary sources, with a binary-symmetric correlation. However, constructing practical codes for the case of non-binary sources with arbitrary correlation remains by and large open. From a practical perspective it is also interesting to consider coding schemes whose performance remains robust to uncertainties in the joint distribution of the sources. In this work we propose the usage of Reed-Solomon (RS) codes for the asymmetric version of this problem. We show that algebraic soft-decision decoding of RS codes can be used effectively under certain correlation structures. In addition, RS codes offer natural rate adaptivity and performance that remains constant across a family of correlation structures with the same conditional entropy. The performance of RS codes is compared with dedicated and rate adaptive multistage LDPC codes (Varodayan et al. '06), where each LDPC code is used to compress the individual bit planes. Our simulations show that in classical Slepian-Wolf scenario, RS codes outperform both dedicated and rate-adaptive LDPC codes under $q$-ary symmetric correlation, and are better than rate-adaptive LDPC codes in the case of sparse correlation models, where the conditional distribution of the sources has only a few dominant entries. In a feedback scenario, the performance of RS codes is comparable with both designs of LDPC codes. Our simulations also demonstrate that the performance of RS codes in the presence of inaccuracies in the joint distribution of the sources is much better as compared to multistage LDPC codes.