Performance evaluation of maximum-likelihood decoded linear binary block codes in AWGN interference using Bonferroni-type and geometrical bounds

The error probability of maximum-likelihood (ML) soft-decision decoded binary block codes rarely accepts exact closed forms. In addition, for long codes ML decoding becomes prohibitively complex. Nevertheless, bounds on the performance of ML decoded systems provide insight into the effect of system parameters on the overall system performance in addition to a measure of efficiency of the sub-optimum decoding methods used in practice. In the article, a comprehensive study of a number of lower and upper bounds on the error probability of ML decoding of binary codes over AWGN channel is provided. Bounds considered here are bounds based on the so-called Bonferroni-type inequalities and bounds developed primarily in the light of the geometrical structure of the underlying signal constellations. The interrelationships among the bounds are explored and current tightest bounds at different noise levels are pointed out.