On the Limiting distribution of Lempel Ziv'78 Redundancy for Memoryles Sources

Philippe Jacquet; Wojciech Szpankowski

On the Limiting distribution of Lempel Ziv'78 Redundancy for Memoryles Sources

Abstract

We show that the Lempel Ziv'78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ'78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences. Then we present simplified proofs and extend our analysis of LZ'78 algorithm to include new results on the convergence of moments, moderate and large deviations, and redundancy analysis.

Authors (2)

Philippe Jacquet
- . .
Wojciech Szpankowski prof. dr inż.
- Purdue University .

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Category:: Conference activity
Type:: publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
Title of issue:: Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on strony 1509 - 1513
Language:: English
Publication year:: 2014
Bibliographic description:: Jacquet P., Szpankowski W.: On the Limiting distribution of Lempel Ziv'78 Redundancy for Memoryles Sources// Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on/ : IEEE, 2014, s.1509-1513
Verified by:: Gdańsk University of Technology