Mathematical formalization of algorithm for demodulation by rule of maximum of a posterior probability that minimizes probability of error per digit

The article describes the algorithm for demodulation by rule of maximum of a posteriori probability. This algorithm minimizes the probability of error per digit. Unlike to conventional approaches, during the algorithm description here term “combination” is used. Applied term “combination” means some sequence of transmitted known and unknown symbols. Relationship was derived for probabilities of state and joint probability densities of signal distribution and state (combination) for arbitrary position of transmitted symbols and arbitrary relative memory of channel. Representation of symbols in shift register from right to left provided to compare the contents of shift register with number of state (combination) in the m-ary numerical system. Proposed method makes up for missing link between mathematical description of the algorithm and its realization by computer.