Upper bounds on the reliability function of the Gaussian channelwere derived by Shannon in 1959. Kabatiansky and Levenshtein (1978)obtained a low-rate improvement of Shannon's “minimum-distancebound”. Together with the straight-line bound this provided animprovement upon the sphere-packing bound in a certain range of coderate. In this work we prove a bound better than the KL bound on thereliability function. Employing the straight-line bound, we obtain afurther improvement of Shannon's results. As intermediate results weprove lower bounds on the distance distribution of spherical codes and atight bound on the exponent of Jacobi polynomials of growing degree inthe entire orthogonality segment
展开▼
