A convolutional code performance bound for Fritchman single-error state channel models

This paper addresses hard-decision decoding of convolutional codes for channels with memory using the standard Viterbi (1967) algorithm. A bound to average bit-error probability is developed for a subclass of the single-error state Markov chain channel models introduced by Fritchman (1967). The condition on the Markov state transition matrix under which the bound holds is that the sum of the products of the probabilities of entering and exiting the error-free states does not exceed the probability of remaining in the error state. The bound is a natural generalization of the standard union bound for memoryless binary symmetric channels. An efficient algorithm for computing each term of the bound is sketched