A Derivation of the Source-Channel Error Exponent using Non-identical Product Distributions

TL;DR

This paper derives the source-channel error exponent for a coding scheme with class-based message assignment and class-dependent codeword distributions, showing optimal class choices can achieve the sphere-packing bound in discrete memoryless systems.

Contribution

It introduces a class-based coding scheme and demonstrates that two optimal classes with product distributions suffice to attain the sphere-packing exponent in certain cases.

Findings

Optimal class-based coding scheme achieves sphere-packing exponent.

Two classes with product distributions are sufficient for tight bounds.

Applicable to discrete memoryless systems.

Abstract

This paper studies the random-coding exponent of joint source-channel coding for a scheme where source messages are assigned to disjoint subsets (referred to as classes), and codewords are independently generated according to a distribution that depends on the class index of the source message. For discrete memoryless systems, two optimally chosen classes and product distributions are found to be sufficient to attain the sphere-packing exponent in those cases where it is tight.