Exact Hamming Distortion Analysis of Viterbi Encoded Trellis Coded Quantizers

TL;DR

This paper derives a closed-form expression for the asymptotic expected Hamming distortion in trellis coded quantizers using Viterbi decoding, based on a Markov chain model.

Contribution

It introduces a method to analytically compute the asymptotic Hamming distortion for trellis coded quantizers with Viterbi decoding using Markov chains.

Findings

Closed-form expression for asymptotic Hamming distortion

Application of Markov chains to analyze quantizer performance

Theoretical insight into distortion behavior as sample size grows

Abstract

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.