Fundamental Limits of Lossless Data Compression with Side Information

TL;DR

This paper investigates the fundamental limits of lossless data compression with side information, providing tight finite-blocklength bounds and analyzing the impact of different side information usage scenarios.

Contribution

It establishes general achievability and converse bounds for both reference-based and pair-based compression, including nonasymptotic normal approximations and dispersion analysis.

Findings

Finite-blocklength bounds are tight up to third-order terms.

Reference-based compression has smaller dispersion than pair-based.

Extensions beyond memoryless sources are developed.

Abstract

The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions of the problem: Reference-based compression, when a single side information string is used repeatedly in compressing different source messages, and pair-based compression, where a different side information string is used for each source message. General achievability and converse theorems are established for arbitrary source-side information pairs. Nonasymptotic normal approximation expansions are proved for the optimal rate in both the reference-based and pair-based settings, for memoryless sources. These are stated in terms of explicit, finite-blocklength bounds, that are tight up to third-order terms. Extensions that go significantly beyond the class of memoryless sources are obtained. The relevant source dispersion is identified and its relationship with the conditional varentropy rate is established. Interestingly, the dispersion is different in reference-based and pair-based compression, and it is proved that the reference-based dispersion is in general smaller.