Polynomial representation of burst error statistics

A burst error process is characterized by three variables x,y,z related to a two-state Gilbert-Elliott channel with fifty percent bit error rate in the bad state. The variables x and y describe the Markov process of the model. The variable z reflects the mean bit error rate. On such a channel, the probability of any single error sequence and hence any collection thereof can be represented by polynomials in x, y, z which extends the one-variable description in z applicable for statistically independent errors.