New Developments of Information-Spectrum Theory

信息谱理论的新进展

• 批准号: 13650401
• 负责人: HAN Te sun
• 金额: $ 2.05万
• 依托单位: The University of Electro-Communications
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650401/
• 关键词: Information Theory; Information Spectrum; Quantum Information Theory; Quantum Channel; Universal Coding; Data Compression; 通信路容量; 情報源符号化; 仮説検定; 漸近理論

The biggest significance of the information-spectrum method lies in its generality and simplicity. The aim of our research is to pursue this characteristic of the method and to extend its scope so as to give new lights to several information-theoretical problems for which construction of general theories had been considered to be difficult. Main results are as follows.(1)An extended and translated version of the book Information-Spectrum Methods in Information Theory has been published from Springer-Verlag, which has further developed mathematical foundations of the theory as well as mathematical tools for applications.(2)We have investigated asymptotic properties of the general hypothesis testing problem, which provides a basis of classical/quantum information theory, to clarify the quantum analogue of the information spectrum. This result has been applied to the channel coding problem to elucidate a close relation between universal coding and sufficient statistics.(3)The universal coding problem has been analyzed from an information-spectrum viewpoint, which has given a condition for a source to have a universal code and elucidated a close relation between universal coding and sufficient statistics.(4)We have investigated from an information-spectrum viewpoint the "folklore" of information theory that the output sequence seems to be almost completely random when a data sequence from an arbitrary source is losslessly compressed with the optimal rate, whereby the folklore has been given a clear mathematical expression and a condition for its validity.

信息谱法的最大意义在于它的通用性和简单性。我们研究的目的是追求这一特点的方法，并扩大其范围，从而给新的灯几个信息理论的问题，建设一般的理论一直被认为是困难的。主要结果如下。(1)An Springer-Verlag出版了《信息论中的信息谱方法》一书的扩展和翻译版本，进一步发展了该理论的数学基础以及应用的数学工具。(2)We研究了一般假设检验问题的渐近性质，这为经典/量子信息理论提供了基础，以澄清信息谱的量子模拟。这一结果已被应用到信道编码问题，以阐明通用编码和充分统计之间的密切关系。（3）从信息谱的观点分析了泛码问题，给出了信源具有泛码的条件，阐明了泛码与充分统计量的密切关系。(4)We从信息谱的观点研究了信息论的“民间传说”，即当来自任意源的数据序列以最佳速率进行有损压缩时，输出序列似乎是几乎完全随机的，由此民间传说已被给出了明确的数学表达式和其有效性的条件。

项目成果

T.Ogawa, H.Nagaoka: "A new proof of the channel coding theorem via hypothesis testing in quantum information theory"Proc.2002 IEEE Int.Symp.Inform.Theory. 73 (2002)

T.Okawa、H.Nagaoka：“通过量子信息理论中的假设检验对信道编码定理的新证明”Proc.2002 IEEE Int.Symp.Inform.Theory。

有村光晴, 長岡浩司: "弱ユニバーサルなFV情報源符号の存在条件について"第25回情報理論とその応用シンポジウム予稿集. 255-258 (2002)

Mitsuharu Arimura，Koji Nagaoka：“论弱通用FV信息源代码的存在条件”第25届信息论及其应用研讨会论文集255-258（2002）。

韓 太舜: "情報スペクトル:あれこれ"電子情報通信学会技術研究報告. IT2003-54, 103・498. 31-39 (2003)

Tae-sun Han：“信息谱：一切”IEICE 技术研究报告。IT2003-54, 103・498 (2003)。

T.S.Han: "Information-Spectrum Methods in Information Theory"Springer-Verlag. 540 (2003)

T.S.Han：“信息论中的信息谱方法”施普林格出版社。

T.S.Han: "A Folklore in Information Theory"Proc.3rd Asian-European Workshop on Information Theory. 61-63 (2003)

T.S.Han：“信息论中的民间传说”Proc.第三届亚欧信息论研讨会。