任意信源的一类渐近均匀分割性定理的研究

A class of asymptotic equipartition property theorems for arbitrary discrete information source

研究了任意信源在可列状态空间下的Shannon-McMillan定理.采用构造相容分布与非负上鞅的方法结合一些重要不等式,研究任意随机变量序列相对熵密度的强极限定理,即渐近均匀分割性.得出了若干任意信源、m阶马氏信源、无记忆信源的渐进均匀分割性定理,并将已有的关于离散信源的结果进行了推广.

A class of Shannon-McMillan theorems for the arbitrary information source was studied. The strong limit theorems for relative entropy densities of the sequence of arbitrary random variables were discussed by constructing the compatible distribution, nonnegative superior martingale, and the important inequalities. As corollaries, some asymptotic equipartition property theorems for arbitrary information source, m-order Markov information source, and non-memory information source were obtained. Moreover, some obtained results for the discrete information source were extended.