Optimal Universal Lossless Compression with Side Information

TL;DR

This paper develops and proves the optimality of new Lempel-Ziv based algorithms for lossless data compression with shared side information, improving compression rates for stationary processes.

Contribution

It introduces fixed-length and variable-length parsing LZ algorithms with side information, demonstrating their optimality and proposing improvements for better compression efficiency.

Findings

Fixed-length-parsing LZ with side info is optimal for stationary processes.

Modified variable-length-parsing LZ with side info is asymptotically optimal for stationary and ergodic processes.

Strategies to reduce data compression rate are proposed.

Abstract

This paper presents conditional versions of Lempel-Ziv (LZ) algorithm for settings where compressor and decompressor have access to the same side information. We propose a fixed-length-parsing LZ algorithm with side information, motivated by the Willems algorithm, and prove the optimality for any stationary processes. In addition, we suggest strategies to improve the algorithm which lower the data compression rate. A modification of a variable-length-parsing LZ algorithm with side information is proposed and proved to be asymptotically optimal for any stationary and ergodic processes.