树上随机场的渐近等分性质

ASYMPTOTIC EQUIP ARTITION PROPERTY FOR RANDOM FIELDS ON TREES

摘要: 本文对定义在Bethe树图上的自同构不变和正则的随机场证明了渐近等分性质,然后应用此性质证明了该模型的信源编码定理,文中还讨论了树上随机场的遍历性,正则性和渐近等分性的相互关系.

Abstract: We prove the asymptotic eqaipartition property （AEP） for an automorphism-invariant and regular random field on a Bethe tree. It is then applied to prove the source coding theorem for this model. Eolations among ergodicity, regularity and the ASP are also discussed.