Enumeration of Markov chains and burst error statistics for finite state channel models

The analysis of a communication system operating over finite state channel (FSC) models includes the calculation of the probability of subsets of error sequences. These probabilities are known as burst error statistics. The study of the statistical description of the error process has immediate applications in the modeling of real channels and in the design of coding schemes for channels with memory. In this paper, we present a method to derive analytic expressions for burst error statistics of FSC models with an arbitrary number of states. We follow the theory of enumeration of constrained sequences to obtain an expression for the generating series which enumerates all permissible error sequences that constitute the burst event of interest. We will show that the probability of this event is obtained by acting on the generating series with a linear mapping. Such an approach allows the derivation of various burst error statistics used in the design of a coded system for FSC models.