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1998 Fiscal Year Final Research Report Summary

Applied Functional Analysis related to Mathematical Information Theory

Research Project

Project/Area Number 09640195
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionYAMAGUCHI UNIVERSITY

Principal Investigator

YANAGI Kenjiro  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (90108267)

Co-Investigator(Kenkyū-buntansha) YANAGIHARA Hiroshi  Yamaguchi University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30200538)
OKADA Mari  Yamaguchi University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (40201389)
KURIYAMA Ken  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (10116717)
MATSUNO Yoshimasa  Yamaguchi University, Faculty of Engineering, Professor, 工学部, 教授 (30190490)
Project Period (FY) 1997 – 1998
KeywordsInformation Theory / Gaussian Channel / Capacity / Feedback / Gaussian Noise / Upper Bound / Average Power Constraint / Shannon Theory
Research Abstract

The mathematical information theory was originally founded by C.E.Shannon in 1948. Since then, it has developed the mathematical foundations to make the communication systems certain, In this research we have five results on the finite block length capacity of discrete time Gaussian chanAels with feedback.
1.We gave the useful upper bound to feedback capacity C_<n, FB> (P) when the power constraint P is relatively large.
2.We gave the useful upper bound to feedback capacity C_<n, FB> (P) when the power constraint P is relatively small.
3.We refined the upper bound to feedback capacity given by Cover and Pombra in 1989. That is, for any alpha > 0 and any P> 0,
4.We solved the conjecture about feedback capacity given by Cover in 1987 in the case of n = 2. That is,
5.We gave some self-inequalities of feedback capacity, which can be applied to upper bound to capacity of blockwise white Gaussian channel with feedback. That is, for any 0 < alpha <less than or equal> 1 and any
In future we will try to prove the concavity of feedback capacity as the function of power constraint.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] 柳 研二郎: "フィードバックをもつ離散時間ガウス型通信路について" 京都大学数理解析研究所講究録. 980. 150-161 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Han Wu Chen: "On the Cover's conjecture on capacity of Gaussian channel with feedback" IEICE Trans.Fundamentals. E80-A. 2272-2275 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kenjiro Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback, III" Bull.Kyushu Inst.Tech., Pure and Applied Mathematics. 45. 1-8 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 陳 漢武: "Cover の conjecture に関連した結果" 京都大学数理解析研究所講究録. 1039. 111-117 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 柳 研二郎: "無限次元空間上の確率測度に関連する再生核ヒルベルト空間の役割-連続時間ガウス型通信路への応用をにらんで-" 京都大学数理解析研究所講究録. 1067. 108-117 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Han Wu Chen: "Refinements of the half-bit and factor-of-two bound for capacity in Gaussian channe〓 with feedback" IEEE Trans.Information Theory. (掲載決定).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Kenjiro Yanagi: "On discrete time Gaussian channel with feedback (in Japanese)" Lecture Notes in RIMS,Kyoto University (Kokyuroku). vol.980. 150-161 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Han Wu Chen: "On the Cover's conjecture on capacity of Gaussian channel with feedback" IEICE Trans.Fundamentals. vol.E80-A. 2272-2275 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kenjiro Yanagi: "An upper bound to the capacity of discrete time Gaussian channel with feedback, III" Bull.Kyushu Inst.Tech., Pure and Applied Mathematics. vol.45. 1-8 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Han Wu Chen: "On the results related to Cover's conjecture (in Japanese)" Lecture Notes in RIMS,Kyoto University (Kokyuroku). vol.1039. 111-117 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kenjiro Yanagi: "The use of reproducing kernel Hilbert spaces related to probability measures on infinite dimensional spaces (in Japanese)" Lecture Notes in RIMS,Kyoto University (Kokyuroku). vol.1067. 108-117 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Han Wu Chen: "Refinements of the half-bit and factor-of-two bound for capacity in Gaussian channels with feedback" IEEE Trans.Information Theory. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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