This article gives a self-contained analysis of the performance of the Lempel-Ziv compression algorithm on (hidden) Markovian sources. Specifically we include a full proof of the assertion that the compression rate approaches the entropy rate of the chain being compressed.
Cite
@article{arxiv.1910.00941,
title = {A Self-contained Analysis of the Lempel-Ziv Compression Algorithm},
author = {Madhu Sudan and David Xiang},
journal= {arXiv preprint arXiv:1910.00941},
year = {2019}
}