Asymptotic equipartition property for a Markov source having ambiguous alphabet

TL;DR

This paper extends the asymptotic equipartition property to Markov sources with ambiguous alphabets, providing a new theoretical framework based on graph parameters and confusability graphs.

Contribution

It introduces a generalized AEP for ambiguous alphabets and connects it to graph entropy rate for Markov sources with distinguishability relations.

Findings

Proves AEP for irreducible stationary Markov sources with ambiguous alphabets.

Provides a graph-theoretic interpretation of the source's entropy rate.

Links asymptotic behavior to the Shannon capacity and confusability graphs.

Abstract

We propose a generalization of the asymptotic equipartition property to discrete sources with an ambiguous alphabet, and prove that it holds for irreducible stationary Markov sources with an arbitrary distinguishability relation. Our definition is based on the limiting behavior of graph parameters appearing in a recent dual characterization of the Shannon capacity, evaluated at subgraphs of strong powers of the confusability graph induced on high-probability subsets. As a special case, our results give an information-theoretic interpretation of the graph entropy rate of such sources.