On the universality of the LZ-based decoding algorithm

Author

Lapidoth, Amos ; Ziv, Jacob

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA

Volume

44

Issue

5

fYear

1998

fDate

9/1/1998 12:00:00 AM

Firstpage

1746

Lastpage

1755

Abstract

A universal decoder for a family of channels is a decoder that can be designed without prior knowledge of the particular channel in the family over which transmission takes place, and it yet attains the same random-coding error exponent as the optimal decoder tuned to the channel in use. We study Ziv´s (1985) decoding algorithm, which is based on Lempel-Ziv (1978) incremental string parsing, and demonstrate that while it was originally proposed as a universal decoder for the family of finite-state channels with deterministic (but unknown) transitions, it is in fact universal for the broader class of all finite-state channels. We also demonstrate that the generalized likelihood decoder may not be universal even for finite families for which a universal decoder always exists

Keywords

coding errors; decoding; probability; telecommunication channels; LZ-based decoding algorithm; Lempel-Ziv incremental string parsing; Ziv decoding algorithm; deterministic transitions; error probability; finite-state channels; generalized likelihood decoder; maximum likelihood decoder; optimal decoder; random-coding error exponent; receiver design; transmission channel; universal decoder; Algorithm design and analysis; Career development; Computer errors; Convergence; Engineering profession; Jacobian matrices; Maximum likelihood decoding; Terminology;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.705554

Filename

705554