Analogy and duality between random channel coding and lossy source coding

TL;DR

This paper unifies the analysis of random coding exponents in channel and lossy source coding, revealing a duality and extending exponents to various decoding scenarios with explicit formulas.

Contribution

It introduces a unified framework for random coding exponents in both channel and source coding, highlighting their duality and extending to erasure and list decoding.

Findings

Channel decoding error exponent equals lossy source encoding success exponent.

Correct-decoding exponent corresponds to encoding failure exponent.

Explicit forms of exponents for various decoding strategies are derived.

Abstract

Here we write in a unified fashion (using "R(P, Q, D)") the random coding exponents in channel coding and lossy source coding. We derive their explicit forms and show, that, for a given random codebook distribution Q, the channel decoding error exponent can be viewed as an encoding success exponent in lossy source coding, and the channel correct-decoding exponent can be viewed as an encoding failure exponent in lossy source coding. We then extend the channel exponents to arbitrary D, which corresponds for D > 0 to erasure decoding and for D < 0 to list decoding. For comparison, we also derive the exact random coding exponent for Forney's optimum tradeoff decoder.