Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels

TL;DR

This paper introduces a linear-codes-based lossless joint source-channel coding scheme for multiple-access channels, analyzing its theoretical properties and proposing a generalized puncturing method for flexible rate coding.

Contribution

It develops a new framework using the code-spectrum approach for designing and analyzing lossless JSCC schemes with linear codes for MACs, including novel rate adaptation techniques.

Findings

Linear codes with good joint spectra can approach capacity limits.

Systematic codes with good spectra have rate constraints related to alphabet size.

Generalized puncturing enables flexible rate coding with a single low-rate code.

Abstract

A general lossless joint source-channel coding (JSCC) scheme based on linear codes and random interleavers for multiple-access channels (MACs) is presented and then analyzed in this paper. By the information-spectrum approach and the code-spectrum approach, it is shown that a linear code with a good joint spectrum can be used to establish limit-approaching lossless JSCC schemes for correlated general sources and general MACs, where the joint spectrum is a generalization of the input-output weight distribution. Some properties of linear codes with good joint spectra are investigated. A formula on the "distance" property of linear codes with good joint spectra is derived, based on which, it is further proved that, the rate of any systematic codes with good joint spectra cannot be larger than the reciprocal of the corresponding alphabet cardinality, and any sparse generator matrices cannot yield linear codes with good joint spectra. The problem of designing arbitrary rate coding schemes is also discussed. A novel idea called "generalized puncturing" is proposed, which makes it possible that one good low-rate linear code is enough for the design of coding schemes with multiple rates. Finally, various coding problems of MACs are reviewed in a unified framework established by the code-spectrum approach, under which, criteria and candidates of good linear codes in terms of spectrum requirements for such problems are clearly presented.