Tree encoding for symmetric sources with a distortion measure

Author

Gallager, Robert G.

Volume

20

Issue

1

fYear

1974

fDate

1/1/1974 12:00:00 AM

Firstpage

65

Lastpage

76

Abstract

A simple algorithm is developed for mapping the outputs of a source into the set of code sequences generated by a tree code. The algorithm is analyzed for a special case in which the source produces discrete independent equiprobable letters, and the distortion measure satisfies a symmetry condition. Letting $R$ be the code rate and $D^{\\ast }$ be the minimum average distortion for that rate as given by Shannon\´s rate-distortion theorem, we show that the algorithm is capable of achieving average distortion as close to $D^{\\ast }$ as desired. Furthermore an upper bound is developed on the average amount of computation for the algorithm. Asymptotically as the average distortion $< d>$ approaches the theoretical limit $D^{\\ast }$ , the bound on average computation has the form $\\exp [a/ \\sqrt {< d> - D^{\\ast } }]$ for some constant $a$ .

Keywords

Rate-distortion theory; Tree codes; Algorithm design and analysis; Constraint theory; Data compression; Decoding; Distortion measurement; Encoding; Rate distortion theory; Rate-distortion; Speech analysis; Upper bound;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1974.1055166

Filename

1055166