Subset-Universal Lossy Compression

TL;DR

This paper proves the asymptotic existence of subset-universal lossy source codes that perform well across various rates and sources, ensuring near-optimal distortion for most codeword subsets.

Contribution

It introduces the concept of subset-universal lossy codes and proves their asymptotic existence for discrete memoryless sources and all sources with the same alphabet.

Findings

Existence of subset-universal lossy codes for discrete memoryless sources.

Codes achieve distortion close to the rate-distortion function for most subsets.

Universal applicability across sources with the same alphabet.

Abstract

A lossy source code $\mathcal{C}$ with rate $R$ for a discrete memoryless source $S$ is called subset-universal if for every $0<R'< R$, almost every subset of $2^{nR'}$ of its codewords achieves average distortion close to the source's distortion-rate function $D(R')$. In this paper we prove the asymptotic existence of such codes. Moreover, we show the asymptotic existence of a code that is subset-universal with respect to all sources with the same alphabet.