Performance of LZ algorithms on individual sequences

Author

Shields, Paul C.

Author_Institution

Dept. of Math., Toledo Univ., OH, USA

Volume

45

Issue

4

fYear

1999

fDate

5/1/1999 12:00:00 AM

Firstpage

1283

Lastpage

1288

Abstract

The performance of three versions of the Lempel-Ziv (1976) algorithm on individual sequences is investigated. It is shown that as the restart length goes to infinity, each compresses an individual sequence as well as any block-to-variable finite-state information lossless algorithm, and that the same conclusion holds for sliding-window LZ as the window width goes to infinity. Examples are given showing that an infinite-memory version outperforms such finite-memory forms and that such finite-memory forms can compress more than the Ziv (1978) entropy, which is the best compression attainable by finite-state block-to-block codes that have vanishing probability of error

Keywords

binary sequences; block codes; data compression; entropy; error statistics; LZ algorithms performance; Lempel-Ziv algorithm; Ziv entropy; block-to-variable lossless algorithm; finite-memory; finite-state block-to-block codes; finite-state information lossless algorithm; infinite-memory; restart length; sequences; sliding-window LZ; vanishing error probability; window width; Computational complexity; Data compression; Decoding; Entropy; Feedback; H infinity control; Notice of Violation; Shift registers; Source coding;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.761286

Filename

761286