The redundancy and distribution of the phrase lengths of the fixed-database Lempel-Ziv algorithm

Author

Wyner, Abraham J.

Author_Institution

Dept. of Stat., Stanford Univ., CA, USA

fYear

1994

fDate

27 Jun-1 Jul 1994

Firstpage

8

Abstract

The fixed-database version of the Lempel-Ziv algorithm (FDLZ) closely resembles many versions that appear in practice. We ascertain several key asymptotic properties of the algorithm as applied to sources with finite memory. First we determine that for a dictionary of size n, the algorithm achieves a redundancy equal to H log log n/log n, where H is the entropy of the process. This is the first, non-trivial, lower bound on any Lempel-Ziv type compression scheme. We then find the limiting distribution (normal) and all moments of the lengths of the phrases

Keywords

data compression; entropy; normal distribution; redundancy; source coding; Lempel-Ziv type compression; asymptotic properties; dictionary; entropy; finite memory sources; fixed-database Lempel-Ziv algorithm; limiting distribution; lower bound; moments; normal distribution; phrase lengths; redundancy; source coding; Algorithm design and analysis; Decoding; Dictionaries; Encoding; Entropy; Performance analysis; Probability distribution; Random sequences; Statistical distributions; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 1994. Proceedings., 1994 IEEE International Symposium on

Conference_Location

Trondheim

Print_ISBN

0-7803-2015-8

Type

conf

DOI

10.1109/ISIT.1994.394963

Filename

394963