The Gaussian isoperimetric inequality and decoding error probabilities for the Gaussian channel

This paper derives an upper bound on the probability of a decoding error after maximum likelihood decoding for the additive white Gaussian noise (AWGN) channel. The bound involves only two basic code parameters : the minimum Euclidean distance D and the critical noise value. For this purpose we bring in a new tool, namely the Gaussian isoperimetric inequality, which does not seem to have ever been used in this context before.