The Likelihood Encoder for Lossy Compression

TL;DR

This paper explores the likelihood encoder's role in lossy source compression, demonstrating its effectiveness through simple proofs and non-asymptotic analysis across various classical source coding scenarios.

Contribution

It introduces the likelihood encoder as a unified approach for classical source coding problems, providing new achievability proofs and non-asymptotic bounds.

Findings

Simplified achievability proofs for rate-distortion and Wyner-Ziv problems

Non-asymptotic bounds on excess distortion

Relation to random binning techniques

Abstract

A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma yields simple achievability proofs for classical source coding problems. The cases of the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic analysis is used for the point-to-point case to examine the upper bound on the excess distortion provided by this method. The likelihood encoder is also related to a recent alternative technique using properties of random binning.