An equivalent Markov model for burst errors in digital channels

Abstract

A hidden Markov model for burst errors is specified by a probability transition matrix P, an initial probability vector p, and the state dependent probability of error matrix B. Several procedures are available for estimating P, p and B from a given error (observation) sequence. However, even with some restrictions on the structure of the underlying Markov models, the estimation procedures are computationally intensive particularly when the observation sequence contains long strings of identical symbols. We show that, under some mild assumptions, a Markov model with an arbitrary transition matrix P is equivalent to a Markov model with a unique "block diagonal" transition matrix /spl Lambda/. We also present a computationally very efficient algorithm for estimating /spl Lambda/ from a set of observation using a modified Baum-Welch (1972) algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>