Markov Channels are Asymptotically Mean Stationary

Abstract

A type of discrete channel is defined which includes the finite-state channel of Blackwell et al. (Ann. Math. Statist., 29 (1958), pp. 1209–1220) and the finite-state source encoder of Shannon (Bell System Tech. J., 27 (1948), pp. 379–423, 623–656) as special cases. It is shown that if the input source to the Markov channel is asymptotically mean stationary in the sense of Gray and Kiefler, then the resulting input-output pair measure is asymptotically mean stationary also. An application to probability theory is given regarding the asymptotic behavior of a sequence of random stochastic matrices.