Theory of optimum M-ary laser detection

An upper bound on the average error probability of all possible M-ary optical systems, using large-average photon statistics, has been derived. This bound clearly indicates the superiority of the M-ary system over the binary one in terms of allowable transmission rates below which the error rate decreases exponentially with code-block length. A probabilistic solution for the problem of efficient signal selection has been found and demonstrated with a simple illustration.