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To the Question of Almost Maximum-Likelihood Decoding

Evseev’s lemma claims that if we use the decoding by a standard array and use coset leaders having the weight not greater than Gilbert-Varshamov distance then the probability of error decoding will become not greater than the probability of error decoding of maximum-likelihood multiplied by two. However, the estimation of tightness of this bound is an open problem. In this work we perform the estimation of the accuracy of Evseev’s lemma on the example of several linear random codes by simulating them in a binary-symmetric channel.