... thank the referee for hisvaluable suggestions. Correspondence author: K. Wang, main research interest is strong limittheory in probability theory. D. Zong main research interest is intelligent algorithm.References1 ... Shannon-McMillan theorems for the random field on the tree graph see 4. The tree models have recentlydrawn increasing interest from specialists in physics, probability and information theory.Berger ... erger, Information Measures for Discrete Random Fields, Science Press, Beijing, China, 1998.5 T. Berger and Z. X. Ye, “Entropic aspects of random fields on trees,” IEEE Transactions on InformationTheory,...