A Normal Sequence Compressed by PPM$^*$ but not by Lempel-Ziv 78
Data Structures and Algorithms
2021-01-21 v1 Information Theory
math.IT
Abstract
In this paper we compare the difference in performance of two of the Prediction by Partial Matching (PPM) family of compressors (PPM and the original Bounded PPM algorithm) and the Lempel-Ziv 78 (LZ) algorithm. We construct an infinite binary sequence whose worst-case compression ratio for PPM is , while Bounded PPM's and LZ's best-case compression ratios are at least and respectively. This sequence is an enumeration of all binary strings in order of length, i.e. all strings of length followed by all strings of length and so on. It is therefore normal, and is built using repetitions of de Bruijn strings of increasing order
Keywords
Cite
@article{arxiv.2009.04827,
title = {A Normal Sequence Compressed by PPM$^*$ but not by Lempel-Ziv 78},
author = {Liam Jordon and Philippe Moser},
journal= {arXiv preprint arXiv:2009.04827},
year = {2021}
}