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| 任意信源的一类广义Shannon-McMillan定理 |
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王康康,叶慧,李芳
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1. 江苏科技大学数理学院,江苏,镇江,212003
2. 安徽师范大学数学计算机科学学院,安徽,芜湖,241000
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| 摘要: |
| 本文研究了任意信源随机和相对熵密度的强极限定理.利用构造相容分布与非负上鞅的方法,获得了m阶马氏信源的随机Shannon-McMillan定理,将已有的关于离散信源的结果加以推广. |
| 关键词: Shannon-McMillan定理 相容分布 任意信源 m阶马氏信源 相对熵密度 |
| DOI： |
| 分类号:O211.6 |
| 基金项目:江苏省高校自然科学基础研究项目，江苏省自然科学基础研究项目 |
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| A CLASS OF GENERALIZED SHANNON-MCMILLAN THEOREMS FOR ARBITRARY DISCRETE INFORMATION SOURCE |
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WANG Kang-kang,YE Hui,LI Fang
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WANG Kang-kang~1,YE Hui~1,LI Fang~2 (1.Dept.of Math.,Jiangsu University of Science and Technology,Zhenjiang 212003,China) (2.School of Math.and Computer Science,An'hui Normal University,Wuhu 241000,China)
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| Abstract: |
| In this article,a class of strong limit theorems for the relative entropy densities of random sum of arbitrary information source is discussed.By constructing the joint distribution and nonnegative super martingales,some Shannon-McMillan theorems for arbitrary information source and mth-order Markov information source are obtained and some known results for the discrete information source are extended. |
| Key words: Shannon-McMillan theorem the compatible distribution arbitrary information source relative entropy density mth-order Markov information source |
