Computing the weight distribution of a set of points obtained by scaling, shifting, and truncating a lattice

Author

Khandani, Amir K. ; Kabal, Peter ; Dubois, Eric

Author_Institution

Dept. of Electr. & Comput. Eng., Waterloo Univ., Ont., Canada

Volume

41

Issue

5

fYear

1995

fDate

9/1/1995 12:00:00 AM

Firstpage

1480

Lastpage

1482

Abstract

A method is developed to compute the weight distribution of a set of points obtained from a lattice. The lattice is scaled (with possibly nonequal factors) along different dimensions, is shifted to an arbitrary point, and its lower dimensional subspaces are truncated within given shaping regions. Each branch in the lattice trellis diagram is labeled by the weight distribution of the corresponding coset incorporating the effects of scaling, shifting, and truncation. The weight distribution is obtained by multiplying the weight distribution of the serial branches and then adding the result over parallel paths

Keywords

geometric codes; lattice theory; source coding; trellis codes; geometrical source coding; lattice trellis diagram; lattice truncation; lower dimensional subspaces; parallel paths; scaling; serial branches; set of points; shifting; weight distribution; Councils; Distributed computing; Joining processes; Lattices; Source coding; Telecommunications; Vector quantization;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.412692

Filename

412692