Universal Variable-to-Fixed Length Lossy Compression at Finite Blocklengths

TL;DR

This paper introduces a universal variable-to-fixed length lossy compression scheme for memoryless sources, optimizing codebook design to achieve near-optimal rates at finite blocklengths.

Contribution

It proposes a novel dictionary construction based on type class coverings and derives the third-order asymptotics of the psilon-coding rate for large dictionaries.

Findings

Achieves asymptotic psilon-coding rate with third-order precision.

Uses boundary type class coverings for dictionary design.

Provides theoretical analysis for finite blocklength performance.

Abstract

We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence is within a specified distortion of a dictionary codeword, the index of the codeword is emitted as the reproduced string. Our proposed dictionary consists of coverings of type classes in the boundary of transition from low to high empirical lossy rate. We derive the asymptotics of the \epsilon-coding rate (up to the third-order term) of our coding scheme for large enough dictionaries.