On the Performance of Lossless Joint Source-Channel Coding Based on Linear Codes for Multiple-Access Channels

A general lossless joint source-channel coding scheme based on linear codes and random interleavers for multiple-access channels 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 good joint spectrum can be used to establish limit-approaching joint source-channel coding schemes for correlated general sources and general multiple-access channels, where the joint spectrum of the code is a generalization of the input-output weight distribution. Some properties of linear codes with good joint spectrums are investigated. A formula on the “distance” property of good linear codes is derived, and based on this formula, it is further proved that the rate of a good systematic code can not be larger than a constant rate and sparse generator matrices can not yield good linear codes. The problem of designing variable rate coding schemes is also discussed. A novel idea called “generalized puncturing” is presented, and hence one good low rate linear code is enough for the design of variable rate coding schemes. Finally, based on the results of this paper and previous literatures, the criteria and candidates of good linear codes for various problems of multiple-access channels are reviewed in a unified framework by the code-spectrum approach. Index Terms Code spectrum, correlated sources, multiple-access channels, information spectrum, linear codes, lossless joint source-channel coding, puncturing. This work was supported in part by the Natural Science Foundation of China under Grant NSFC-60472079 and by the Chinese Specialized Research Fund for the Doctoral Program of Higher Education under Grant 2004-0335099. S. Yang and P. Qiu are with the Department of Information Science & Electronic Engineering, Zhejiang University, Hangzhou, 310027, China(email: [email protected]; [email protected]). SUBMITTED TO IEEE TRANSACTIONS ON INFORMATION THEORY (VERSION: NOVEMBER 27, 2006) 1 On the Performance of Lossless Joint Source-Channel Coding Based on Linear Codes for Multiple-Access Channels