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

A. Ashikhmin, A. Barg, S. Litsyn

Research output: Contribution to journalConference articlepeer-review

Abstract

Upper bounds on the reliability function of the Gaussian channel were derived by Shannon in 1959 [1]. Kabatiansky and Levenshtein [2] 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.

Original languageEnglish
Pages (from-to)458
Number of pages1
JournalIEEE International Symposium on Information Theory - Proceedings
StatePublished - 2000
Externally publishedYes
Event2000 IEEE International Symposium on Information Theory - Serrento, Italy
Duration: 25 Jun 200030 Jun 2000

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