关于Shannon-Mcmillan定理的若干研究(Ⅱ)

数学物理学报 ›› 1997, Vol. 17 ›› Issue (2): 176-183.

关于Shannon-Mcmillan定理的若干研究(Ⅱ)

刘文¹, 杨卫国²

1 河北工业大学天津 300130;
2 河北煤炭建筑工程学院邯郸 056038

收稿日期:1995-05-16 修回日期:1995-11-17 出版日期:1997-04-26 发布日期:1997-04-26
基金资助:
河北省自然科学基金

Some Researches of Shannon-Mcmillan Theorem(Ⅱ)

Liu Wen¹, Yang Weiguo²

1 Hebei University of Technology, Tianjin 300130;
2 Hebei Mining and Civil Engineering Institute, Handan 056038

Received:1995-05-16 Revised:1995-11-17 Online:1997-04-26 Published:1997-04-26

摘要/Abstract

摘要： 该文通过概率空间上的任意分布列与独立分布列比较,研究任意随机变量序列相对熵密度用不等式给出的强极限定理,即小偏差定理,并由此得出若干Shannon-Mcmillan定理,将作者已有的关于离散信源的结果加以推广.

关键词: Shannon-Mcmillan定理, 小偏差定理, 相对熵密度, 离散信源

Abstract: In this paper, a class of small-devitions theorems for the relative entropy densities of the sequence of arbitrary random variables are discussed by comparing between the sequence of arbitrary distributions and the seqence of independent distributions. As corollaries, some Shannon-Mcmillan theorems are obtained and some results for the discrete information source which has been obtained by authors before are extended.

Key words: Shannon-Mcmillan theorem, small-deviations theorem, relative entropy density, discrete information source

刘文, 杨卫国. 关于Shannon-Mcmillan定理的若干研究(Ⅱ)[J]. 数学物理学报, 1997, 17(2): 176-183.

Liu Wen, Yang Weiguo. Some Researches of Shannon-Mcmillan Theorem(Ⅱ)[J]. Acta mathematica scientia,Series A, 1997, 17(2): 176-183.

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