Title :
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
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;
Conference_Titel :
Information Theory and Communications Workshop, 1999. Proceedings of the 1999 IEEE
Conference_Location :
Kruger National Park
Print_ISBN :
0-7803-5268-8
DOI :
10.1109/ITCOM.1999.781434
