Derivation of the fundamental formulas for evaluation of codes on general types of channels

Fritchman's partitioned Markov chain model is used in the performance analysis of various codes on communication channels in order to evaluate the probability Pb(m, n) for the occurrence of a single burst error of length m in a code word of length n, as well as the probability P(m, n) for the occurrence of m error digits in a code word of length n. The derived formulas are used to estimate the performance of error-correcting codes on channels represented by the Gilbert model, the generalized Gilbert model, and the Fritchman model, all having the same average bit-error rate. The effectiveness and computational savings of the derived formulas are demonstrated.