The Asymptotic Equipartition Property for a Nonhomogeneous Markov Information Source

Abstract

In this paper, we study the asymptotic equipartition property (AEP) for a nonhomogeneous Markov information source. We first give a limit theorem for the averages of the functions of two variables of this information source by using the convergence theorem for the martingale difference sequence. As corollaries, we get several limit theorems and a limit theorem of the relative entropy density, which hold for any nonhomogeneous Markov information source. Then, we get a class of strong laws of large numbers for nonhomogeneous Markov information sources. Finally, we prove the AEP for a class of nonhomogeneous Markov information sources.