Lattice and trellis quantization with lattice- and trellis-bounded codebooks-High-rate theory for memoryless sources

Author

Eyuboglu, Vedat M. ; Forney, David G.

Author_Institution

Motorola Codex, Mansfield, MA, USA

Volume

39

Issue

1

fYear

1993

fDate

1/1/1993 12:00:00 AM

Firstpage

46

Lastpage

59

Abstract

High-rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed. The performance of these quantizers is determined by two separable quantities, the granular gain and the boundary gain, which are determined by the shapes of the granular cells and of the support region, respectively. The granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications. Using this duality, it is shown for Gaussian sources that the ultimate achievable boundary gain with high-rate lattice-bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable-rate entropy coding. It is observed that if lattice codebooks can achieve the ultimate granular gain of 0.255 b per dimension, then lattice-bounded lattice codebooks can approach the rate-distortion limit. The performance of lattice quantizers is compared to that of optimum vector quantizers

Keywords

information theory; lattice theory and statistics; trellis codes; vector quantisation; Gaussian sources; High-rate theory; boundary gain; coding gain; data transmission applications; duality; granular gain; lattice quantisation; lattice-bounded lattice codebooks; memoryless sources; nonuniform sources; rate-distortion limit; shaping gain; trellis quantization; trellis-bounded codebooks; vector quantizers; Conferences; Data communication; Entropy coding; Lattices; Modulation coding; Performance gain; Quantization; Rate-distortion; Shape; Source coding; Vector quantization;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.179341

Filename

179341