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A class of small-deviation theorems for the relative entropy densities of arbitrary random field on the generalized Bethe tree are discussed by comparing the arbitrary measure with the Markov measure Q on the generalized Bethe tree. As corollaries, some Shannon-Mcmillan theorems for the arbitrary random field on the generalized Bethe tree, Markov chain field on the generalized Bethe tree are obtained. © 2011 Kangkang Wang and Decai Zong.

Some Shannon-McMillan Approximation Theorems for Markov Chain Field on the Generalized Bethe Tree