Sphere-bound-achieving coset codes and multilevel coset codes

Author

Forney, G. David, Jr. ; Trott, Mitchell D. ; Chung, Sae-Young

Author_Institution

Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

Volume

46

Issue

3

fYear

2000

fDate

5/1/2000 12:00:00 AM

Firstpage

820

Lastpage

850

Abstract

A simple sphere bound gives the best possible tradeoff between the volume per point of an infinite array L and its error probability on an additive white Gaussian noise (AWGN) channel. It is shown that the sphere bound can be approached by a large class of coset codes or multilevel coset codes with multistage decoding, including certain binary lattices. These codes have structure of the kind that has been found to be useful in practice. Capacity curves and design guidance for practical codes are given. Exponential error bounds for coset codes are developed, generalizing Poltyrev´s (1994) bounds for lattices. These results are based on the channel coding theorems of information theory, rather than the Minkowski-Hlawka theorem of lattice theory

Keywords

AWGN channels; block codes; channel coding; decoding; error statistics; group codes; random codes; AWGN channel; Poltyrev´s bounds; additive white Gaussian noise channel; binary lattices; block code; capacity curves; channel coding theorems; code structure; design guidance; error probability; exponential error bounds; group code; infinite array; information theory; multilevel coset codes; multistage decoding; practical codes; random codes; sphere-bound-achieving coset codes; volume per point; AWGN; Additive white noise; Channel coding; Constellation diagram; Constraint theory; Decoding; Gaussian noise; Information theory; Lattices; Legged locomotion;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.841165

Filename

841165