The generalized asymptotic equipartiton property for higher-order non homogeneous markov information source

The asymptotic equipartiton property (AEP) plays a crucial role in information theory, providing a theoretical foundation for understanding and analyzing aspects such as coding, compression, and the reliability of communication systems. In this article, we mainly study the generalized AEP of higher-order non homogeneous Markov information sources by establishing several strong deviation theorems. To achieve this, we first introduce the concepts of generalized sample divergence rate of mth-order non homogeneous Markov information sources. Meanwhile, we give a class of generalized strong deviation theorems for moving average of the functions of m+1 variables for mth-order non homogeneous Markov information sources, and also establish strong deviation theorems and strong limit theorems of the frequencies of occurrence of ordered tuples of states for this Markov information sources. Finally, the generalized AEP for mth-order non homogeneous Markov information sources are establized. Our results also generalize some known results.