On the relation between the code spectrum and the decoding error probability (Q5930865)

The main purpose of this paper is to show how to get lower bounds for the decoding error probability (and, as a corollary, upper bounds for the reliability function \(E(R,A)\)) given some bounds for the code spectrum. For definiteness, the author focuses on a Gaussian channel though the approach can be applied to other channels as well, in particular, to a BSC. Bounds for \(E(R,A)\) thus obtained are better than previously known ones in some range of the rate \(R\).