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Let G be a finite strongly connected aperiodic directed graph in which eachedge carries a label from a finite alphabet A. Then G induces a trellis codedquantizer for encoding an alphabet A memoryless source. A source sequence oflong finite length is encoded by finding a path in G of that length whosesequence of labels is closest in Hamming distance to the source sequence;finding the minimum distance path is a dynamic programming problem that issolved using the Viterbi algorithm. We show how a Markov chain can be used toobtain a closed form expression for the asymptotic expected Hamming distortionper sample that results as the number of encoded source samples increaseswithout bound.

Exact Hamming Distortion Analysis of Viterbi Encoded Trellis Coded Quantizers