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Study of Information Theory Based on Probability Theory

Research Project

Project/Area Number 05452013
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

IHARA Shunsuke  Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (00023200)

Co-Investigator(Kenkyū-buntansha) YOKOI Nideo  Nagoya University, Graduate School of Human Informatics, Professor, 人間情報学研究科, 教授 (50023560)
MORIMOTO Hiroshi  Nagoya University, School of Informatics and Sciences, Assoc.Professor, 情報文化学部, 助教授 (20115645)
ITO Masayuki  Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (60022638)
OZAWA Masanao  Nagoya University School of Informatics and Sciences, Professor, 情報文化学部, 教授 (40126313)
SATO Ken-iti  Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (60015500)
村井 隆文  名古屋大学, 情報文化学部, 教授 (00109266)
長井 英生  名古屋大学, 情報文化学部, 助教授 (70110848)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥6,300,000 (Direct Cost: ¥6,300,000)
Fiscal Year 1995: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1994: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1993: ¥2,300,000 (Direct Cost: ¥2,300,000)
Keywordsinformation theory / spectral analysis of stationary processes / maximum entropy method / large deviation theorem / channel capacity / ガウス型通信路 / 大偏差理論
Research Abstract

We have studied theory of stochastic processes and information theory, and obtained following results.
(1) We investigate the large deviation theorems and their applications. First, we consider a signal detection problem in a continuous time white Gaussian channel. Suppose that one of two stationary signals is transmitted over the channel. Based on the observation of the output, we are required to decide which signal is sent. This is a kind of hypothesis testing problem. Using a large deviation theorem, we have shown that the error probability of the detection goes to zero exponentially fast.
(2) It is known that the maximum entropy method is a method to estimate a spectral density function of a stationary proces. Using a large deviation theorem, we prove a limit theorem which shows that the maximum entropy method is optimal if the sample size is large enough.
(3) Channel capacity, mutual information, and mean squre error play fundamental roles in information theory. We prove some inequalities for these quantities. These inequalities will play important roles in information theory. One of them is as follows. Let C be the feedback capacity of a communication channel with an additive noize Z,and denote by C^* the feedback capacity of the channel with Gaussian noize Z^* having the same covariance as Z.Then it is true that C^* < C < C^* + H (Z ; Z^*), where H (Z ; Z^*) denotes the relative entropy of Z with respect to Z^*.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (31 results)

All Other

All Publications (31 results)

  • [Publications] Shunsuke Ihara: "Some inequalities for channel capacities, mutual informations and mean square errors." IEEE Trans. Information Theory. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S. Ihara, Y. Sakuma: "Signal detection in continuous time white Gaussian channel." Proc. Seventh Japan-Russia Symposium on Prog. Theary and Math. Stat.(to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K. Sato, Gyeong Suck Choi: "Recurrence and transience of operator semi-stable processes." Proc. Japan Acad. Ser. A. 71. 98-100 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Ken-iti Sato: "Time evolution in distributions of Levy processes" Southeast Asian Bulletin of Math.19. 17-26 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Masanao Ozawa: "Mathematical characterizations of measurement statistics." Quantum Communications and Measurement, Plenum. 109-117 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Hiroshi Morimoto: "Sympletic geometry and deformation of infinite dimensional cycles associated to Canchy-Riamamm operators." Tokyo J. Math.18. 1-10 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Ihara: "Some inequalities for channel capacities, mutual informations and mean squre errors" IEEE Trans.Information Theory. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] S.Ihara and Y.Sakuma: "Signal detection in continuous time white Gaussian channel" Proc.Seventh Japan-Russia Symposium on Prob.Theory and Math.Stat.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sato and Gyeong Suck Choi: "Recurrence and transience of operator semi-stable processes" Proc.Japan Acad.71. 98-100 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Sato: "Time evolution in distribution of Levy processes" Southeast Asian Bulletin of Math.19. 17-26 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Ozawa: "Mathematical characterizations of measurement statistics" Quantum Communications and Measurement (Plenum). 109-117 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] H.Morimoto: "Sympletic geometry and deformation of infinite dimensional cycles associated to Cauchy-Riemann operators" Tokyo J.Math.18. 1-10 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] Shunsuke Ihara: "Some inegualities for chaunel capacilies,mutual informations and mean sguare errors." IEEE Trans.Information Theary. (to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] S.Ihara,Y.Sakuma: "Signal detection in continucus time white Gaussian channel." Prec.Seventh Japan-Russion Symposium on Prob.Theory and Math.Stat.(to appear).

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Sato,Gyeong Suck Choi: "Recurrence and transience of operator semi-stable processes." Proc.Japan Aad.Ser.A. 71. 98-100 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Keniti Sato: "Time evolution in clistributions of Levy prccesses" Sautheast Asian Bulletin of Math.19. 17-26 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Masanao Ozawa: "Mathematical characterizations of measurcment statistics." Quantum Communications and Measurement,Plenum. 109-117 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Hiroshi Morimoto: "Sympletic geometry and defor mation of infinite dimeusioucl cycles assctiated to Comchy-Riamamm operaturs." Tokyo J.Math.18. 1-10 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] Shunsuke Ihara: "Coding Theosems for a continuous-time Gaussian channel with feedback." IEEE Trans.Information Theory. IT-40. 2041-2045 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Ken-iti Sato: "Multimodal convolutions of unimodal infinitely divisiale distributions." Teor.Veroyat.Primen.39. 403-415 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] K.Sato,T.Watanabe,M.Yamazato: "Recurrence conditions for multidimensional processes of Ornstein-cihleubeck type." J.Math.Soc.Japan. 46. 245-265 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Hideo Nagai: "Bellman equations of risk sensitive control." SIAM J.on Control and Optimization. (to appear).

    • Related Report
      1994 Annual Research Report
  • [Publications] Masayuki Ito: "On the spectral synthesis of potentials with respect to continuous function-kernels." Nagoya Math.J.(to appear).

    • Related Report
      1994 Annual Research Report
  • [Publications] Hideo Yokoi: "Solvability of the Diophan tine equation x^2-Dy^2=±2 and new invariants for neal quadratic fields." Nagoya Math.J.134. 137-149 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Ken-iti Sato: "Convolution of unimodal distributions can produce any number of modes." Ann.Probability. 21. 1543-1549 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Ken-iti Sato: "Remarks on recurrence criteria for processes of Ornstein-Uhlenbeck Type." Lecture Notes in Mathematics. 1540. 329-340 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Hideo Nagai: "Extremal holomorphic diffusion processes." Potential Analysis. 2. 371-386 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Masanao Ozawa: "Canonical approximate quantum measurements." J.Math.Physics. 34. 5596-5624 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Masayuki Ito: "On the spectral synthesis of potentials with respect to continuous function-kernels." Preprint Series,Dept.of Math,Col.Gen.Edu.,Nagoya U.15. 1-22 (1992)

    • Related Report
      1993 Annual Research Report
  • [Publications] Hideo Yokoi: "New invariants and class number problem in real quadratic fields." Nagoya Math.J.132. 175-197 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Shunsuk Ihara: "Information Theory for Continuous Systems." World Scientific,(Singapore), 308 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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