A new upper bound on the reliability function of the Gaussian channel

Author

Ashikhmin, A. ; Barg, A. ; Litsyn, S.

Author_Institution

Los Alamos Nat. Lab., NM, USA

fYear

1999

fDate

1999

Firstpage

103

Abstract

Upper bounds on the reliability function of the Gaussian channel were derived by Shannon in 1959. Kabatiansky and Levenshtein (1978) obtained a low-rate improvement of Shannon´s “minimum-distance bound”. Together with the straight-line bound this provided an improvement upon the sphere-packing bound in a certain range of code rate. In this work we prove a bound better than the KL bound on the reliability function. Employing the straight-line bound, we obtain a further improvement of Shannon´s results. As intermediate results we prove lower bounds on the distance distribution of spherical codes and a tight bound on the exponent of Jacobi polynomials of growing degree in the entire orthogonality segment

Keywords

Gaussian channels; channel capacity; codes; polynomials; reliability; Gaussian channel; Jacobi polynomials exponent; Shannon´s minimum-distance bound; code rate; distance distribution; lower bounds; reliability function; sphere-packing bound; spherical codes; straight-line bound; tight bound; upper bound; Error probability; Gaussian channels; Gaussian noise; Information theory; Jacobian matrices; Laboratories; Maximum likelihood decoding; Postal services; Signal to noise ratio; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory and Communications Workshop, 1999. Proceedings of the 1999 IEEE

Conference_Location

Kruger National Park

Print_ISBN

0-7803-5268-8

Type

conf

DOI

10.1109/ITCOM.1999.781434

Filename

781434