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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (5): 515-524.doi: 10.3969/j.issn.1005-3085.2019.05.003

• • 上一篇    下一篇

关于非齐次马氏链信源的一个编码定理

周  丹,  汪忠志   

  1. 安徽工业大学数理科学与工程学院，马鞍山  243002
  • 收稿日期:2017-09-27 接受日期:2018-04-13 出版日期:2019-10-15 发布日期:2019-12-15
  • 基金资助:
    国家自然科学基金(11571142)；安徽省自然科学基金(1408085MA04)；安徽省教育厅科研基金(KJ2017A851; KJ2017A420).

A Coding Theorem for Nonhomogeneous Markov Source

ZHOU Dan,  WANG Zhong-zhi   

  1. School of Mathematics & Physics Science and Engineering, Anhui University of Technology, Ma'anshan 243002
  • Received:2017-09-27 Accepted:2018-04-13 Online:2019-10-15 Published:2019-12-15
  • Supported by:
    The National Natural Science Foundation of China (11571142); the Natural Science Foundation of Anhui Province (1408085MA04); the Natural Science Foundation of the Education Department of Anhui Province (KJ2017A851; KJ2017A420).

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摘要： 本文旨在将无记忆离散信源的编码定理推广至非齐次马尔科夫链情形，以扩展无记忆离散信源编码定理的适用范围．利用经典的波莱尔-坎特利引理，建立关于非齐次马尔科夫链延迟平均的强大数定理，应用独立随机信源逼近非齐次马氏信源，从而获得非齐次马氏信源的广义编码定理．最后运用得到的广义编码定理，给出分批数据假设检验问题中可容忍错误概率的最小值的计算方法．

关键词: 非齐次马氏信源, 编码定理, 假设检验, Borel-Cantelli 引理, 一致有界

Abstract: This paper is in order to extend the memoryless discrete source coding theorem to the case of nonhomogeneous Markov chain which leads to a greater application range. Firstly, we establish a strong law of large numbers of a delayed nonhomogeneous Markov chain by the classical Borel-Cantelli lemma. Then, we apply an independent random source to approximate the nonhomogeneous Markov source in order to obtain the general coding theorem of the nonhomogeneous Markov source. Finally, with the help of the general coding theorem of nonhomogeneous Markov source, we propose the a numerical method of the lowest fault tolerance rate in batch data hypothesis test.

Key words: nonhomogeneous markov source, coding theorem, hypothetical test, Borel-Cantelli lemma, unanimously bounded

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