The Dispersion of Mismatched Joint Source-Channel Coding for Arbitrary Sources and Additive Channels

TL;DR

This paper introduces a mismatched joint source-channel coding scheme for arbitrary sources and additive channels, deriving tight second-order and moderate deviations results that generalize previous foundational work.

Contribution

It proposes a novel mismatched coding architecture with UEP and regularized decoding, extending dispersion analysis to a broad class of sources and channels.

Findings

Derived ensemble-tight second-order results.

Established moderate deviations asymptotics.

Generalized dispersion as a linear combination of prior saddle-point problems.

Abstract

We consider a joint source channel coding (JSCC) problem in which we desire to transmit an arbitrary memoryless source over an arbitrary additive channel. We propose a mismatched coding architecture that consists of Gaussian codebooks for both the source reproduction sequences and channel codewords. The natural nearest neighbor encoder and decoder, however, need to be judiciously modified to obtain the highest communication rates at finite blocklength. In particular, we consider a unequal error protection (UEP) scheme in which all sources are partitioned into disjoint power type classes. We also regularize the nearest neighbor decoder so that an appropriate measure of the size of each power type class is taken into account in the decoding strategy. For such an architecture, we derive ensemble-tight second-order and moderate deviations results. Our first-order (optimal bandwidth expansion ratio) result generalizes the seminal results by Lapidoth (1996, 1997). The dispersion of our JSCC scheme is a linear combination of the mismatched dispersions for the channel coding saddle-point problem by Scarlett, Tan and Durisi (2017) and the rate-distortion saddle-point problem by the present authors, thus also generalizing these results.