  Let G be a finite strongly connected aperiodic directed graph in which each
edge carries a label from a finite alphabet A. Then G induces a trellis coded
quantizer for encoding an alphabet A memoryless source. A source sequence of
long finite length is encoded by finding a path in G of that length whose
sequence of labels is closest in Hamming distance to the source sequence;
finding the minimum distance path is a dynamic programming problem that is
solved using the Viterbi algorithm. We show how a Markov chain can be used to
obtain a closed form expression for the asymptotic expected Hamming distortion
per sample that results as the number of encoded source samples increases
without bound.
