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arXiv · 2009.04827

A Normal Sequence Compressed by PPM$^*$ but not by Lempel-Ziv 78

Liam Jordon·Philippe Moser
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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 $0$, while Bounded PPM's and LZ's best-case compression ratios are at least $1/2$ and $1$ respectively. This sequence is an enumeration of all binary strings in order of length, i.e. all strings of length $1$ followed by all strings of length $2$ and so on. It is therefore normal, and is built using repetitions of de Bruijn strings of increasing order

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Liam Jordon, Philippe Moser. 2020-09-10. A Normal Sequence Compressed by PPM$^*$ but not by Lempel-Ziv 78. https://doi.org/10.1007/978-3-030-67731-2_28

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