Finite-state codes

Author

Pollara, Fabrizio ; Mceliece, Robert J. ; Abdel-Ghaffar, Khaled

Author_Institution

Jet Propulsion Lab., Pasadena, CA, USA

Volume

34

Issue

5

fYear

1988

fDate

9/1/1988 12:00:00 AM

Firstpage

1083

Lastpage

1089

Abstract

A class of codes called finite-state (FS) codes is defined and investigated. The codes, which generalize both block and convolutional codes, are defined by their encoders, which are finite-state machines with parallel inputs and outputs. A family of upper bounds on the free distance of a given FS code is derived. A general construction for FS codes is given, and it is shown that in many cases the FS codes constructed in this way have a free distance that is the largest possible. Catastrophic error propagation (CEP) for FS codes is also discussed. It is found that to avoid CEP one must solve the graph-theoretic problem of finding a uniquely decodable edge labeling of the state diagram

Keywords

boundary-value problems; codes; encoding; errors; graph theory; block codes; catastrophic error propagation; convolutional codes; encoders; finite-state codes; finite-state machines; graph-theoretic problem; parallel inputs; parallel outputs; state diagram; upper bounds; Block codes; Convolutional codes; Information theory; Notice of Violation; Random processes; Random variables; Rate distortion theory; Source coding; Stochastic processes; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.21238

Filename

21238