Abstract-In this work, we provide a computable expression for the Kullback-Leibler divergence rate lim ( ) between two time-invariant finite-alphabet Markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions and , respectively. We illustrate it numerically and examine its rate of convergence. The main tools used to obtain the Kullback-Leibler divergence rate and its rate of convergence are the theory of nonnegative matrices and Perron-Frobenius theory. Similarly, we provide a formula for the Shannon entropy rate lim ( ) of Markov sources and examine its rate of convergence.
In REF , an expression for the Kullback-Leibler (KL) divergence rate is derived when the two distributions are Markov chains of arbitrary order, which is a special case of the formulation here.
The Kullback-Leibler divergence rate between Markov sources
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics