Gilbert-Varshamov bound for Euclidean space codes over distance-uniform signal sets

Author

Rajan, B. Sundar ; Subramaniam, L. Venkata ; Bahl, Rajendar

Author_Institution

Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India

Volume

48

Issue

2

fYear

2002

fDate

2/1/2002 12:00:00 AM

Firstpage

537

Lastpage

546

Abstract

In this correspondence, in an extension of Piret´s bound for codes over phase-shift keying (PSK) signal sets, we investigate the application of the Gilbert-Varshamov (GV) bound to a variety of distance-uniform (DU) signal sets in Euclidean space. It is shown that four-dimensional signal sets matched to binary tetrahedral, binary octahedral, and binary icosahedral groups lead to better bounds compared to the bounds for signal sets matched to dicyclic groups with the same number of signal points and comparable symmetric PSK signal sets

Keywords

modulation coding; phase shift keying; DU signal sets; Euclidean space codes; GV bound; Gilbert-Varshamov bound; PSK signal sets; Piret bound; binary icosahedral groups; binary octahedral groups; binary tetrahedral groups; dicyclic groups; distance-uniform signal sets; four-dimensional signal sets; phase-shift keying; signal points; Galois fields; Geometry; Hamming distance; Lead compounds; Mathematics; Notice of Violation; Phase shift keying;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.979331

Filename

979331