Information Spectrum Approach to the Source Channel Separation Theorem

TL;DR

This paper extends the source-channel separation theorem to more general sources and channels using information spectrum methods, relaxing previous constraints and providing broader applicability.

Contribution

It proves a stronger source-channel separation theorem for general sources and channels using information spectrum techniques, including cases with the strong converse property.

Findings

The theorem applies to sources satisfying sphere packing optimality.

The results hold for channels with the strong converse property.

The approach simplifies extensions to other scenarios.

Abstract

A source-channel separation theorem for a general channel has recently been shown by Aggrawal et. al. This theorem states that if there exist a coding scheme that achieves a maximum distortion level d_{max} over a general channel W, then reliable communication can be accomplished over this channel at rates less then R(d_{max}), where R(.) is the rate distortion function of the source. The source, however, is essentially constrained to be discrete and memoryless (DMS). In this work we prove a stronger claim where the source is general, satisfying only a "sphere packing optimality" feature, and the channel is completely general. Furthermore, we show that if the channel satisfies the strong converse property as define by Han & verdu, then the same statement can be made with d_{avg}, the average distortion level, replacing d_{max}. Unlike the proofs there, we use information spectrum methods to prove the statements and the results can be quite easily extended to other situations.