Class-Based Expurgation Attains Csisz\'ar's Expurgated Source-Channel Exponent

TL;DR

This paper demonstrates that partitioning source messages into two classes with class-dependent codeword distributions can achieve Csiszár's expurgated source-channel error exponent, advancing understanding of error bounds in joint source-channel coding.

Contribution

It introduces a class-based expurgation method that attains Csiszár's exponent using only two classes, simplifying previous approaches.

Findings

Two classes suffice to achieve Csiszár's exponent.

Class-dependent codeword distributions improve error exponent bounds.

The method simplifies the design of expurgated codes.

Abstract

This paper studies expurgated error exponents for joint source-channel coding for discrete memoryless sources and channels. We consider a partition of the source messages into classes, where the codeword distributions depend on the class. We show that two carefully chosen classes suffice to achieve Csisz\'ar's expurgated exponent.