The Reliability Function of Lossy Source-Channel Coding of Variable-Length Codes with Feedback

TL;DR

This paper derives the reliability function for variable-length lossy source-channel coding with feedback over DMCs, showing that separate source-channel coding is optimal in this regime.

Contribution

It establishes the exact form of the reliability function for lossy source-channel coding with feedback and proves the optimality of separate coding in this setting.

Findings

Reliability function equals max{0, B(1 - R(D)/C)}.

Separate source-channel coding is optimal.

Provides a closed-form expression for the error exponent.

Abstract

We consider transmission of discrete memoryless sources (DMSes) across discrete memoryless channels (DMCs) using variable-length lossy source-channel codes with feedback. The reliability function (optimum error exponent) is shown to be equal to $\max\{0, B(1-R(D)/C)\},$ where $R(D)$ is the rate-distortion function of the source, $B$ is the maximum relative entropy between output distributions of the DMC, and $C$ is the Shannon capacity of the channel. We show that, in this setting and in this asymptotic regime, separate source-channel coding is, in fact, optimal.