任意信源的一类Shannon-Mcmillan逼近定理

A Class of Shannon-Mcmillan Approximation Theorems for Arbitrary Discrete Information Source

中文关键词:  Shannon-Mcmillan定理  小偏差定理  任意信源  相对熵密度  $m$阶马氏信源.

英文关键词:Shannon-Mcmillan theorem  arbitrary information source  small-deviation theorems  relative entropy density  $m$-order Markov information source.

中文摘要:

      该文通过概率空间上的任意分布与另一任意分布相比较,研究任意随机序列相对熵密度的小偏差定理.并由此得出若干任意信源, $m$阶马氏信源的Shannon-Mcmillan定理.将已有的关于离散信源的结果加以推广.

英文摘要:

      In this paper, a class of small-deviation theorems for the relative entropy densities of the arbitrary stochastic sequence are discussed by comparing two joint distributions. As corollaries, some Shannon-Mcmillan theorems for arbitrary information source, $m$-order Markov information source are obtained and some results for the discrete information source are extended.