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Research on Stochastic Processes and Information Theory

Research Project

Project/Area Number 14540111
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

IHARA Shunsuke  Nagoya University, Graduate School of Information Science, Professor, 情報科学研究科, 教授 (00023200)

Co-Investigator(Kenkyū-buntansha) SATO Junya  Nagoya University, Graduate School of Information Science, Associate Professor, 情報科学研究科, 助教授 (20235352)
MATSUBARA Yo  Nagoya University, Graduate School of Information Science, Associate Professor, 情報科学研究科, 助教授 (30242788)
MATSUMOTO Hiroyuki  Nagoya University, Graduate School of Information Science, Professor, 情報科学研究科, 教授 (00190538)
TSUKIJI Tatsuie  Tokyo Electrical University, School of Eng. and Sci., Associate Professor, 理工学部, 助教授 (70291961)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsGaussian channel / Source coding / Channel coding / Waiting time for string matching / Large deviation theorem
Research Abstract

We have studied on stochastic processes and information theory and obtained the following results.
[1]Error probability for Gaussian channels with feedback.
For the white Gaussian channel with feedback, it is known that the error probability decreases to zero more rapidly than the exponential of any order. Note that the precise proof of this fact is not familiar. We have given a new proof for this fact, not only for the discrete-time case but also for the continuous-time white Gaussian channel with feedback.
[2]Error exponents for the source coding with distortion.
For the lossy source coding, if the coding rate is greater than the rate distortion function, Marton (1974) proved that, for the stationary memoryless source with finite alphabet, the optimum error probability, namely the minimum probability of distortion exceeding a prescribed level, decreases to zero exponentially fast and gave a formula for the error exponent. We extended the Marton's results to the stationary memoryless sources with general alphabet and, proved that the Marton's formula remains true even if the alphabet is not finite.
[3]Asymptotic behavior of probability of string matching.
Applying a large deviation theorem to Gaussian stationary processes, we obtained formulas of the asymptotic behavior of probability of string matching and of the waiting time for string matching.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] S.Ihara, M.Kubo: "The asymptotics of string matching probabilities for Gaussian random sequences"Nagoya Math.Journal. 166. 39-54 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara: "Information transmission over Gaussian channels with feedback"Proc. Third Asian-European Workshop on Inform. Theory. 53-56 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara, Lin Gui Xin: "Error exponents for discrete-time white Gaussian channel with feedback"Proc. Meijo Winter School on Quantum Inform. and Complexity. (To appear). (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto, M.Yor: "Interpretation via Brownian motion of some independence properties between GIG and gamma variables"Stat. Prob. Lett.. 61. 253-259 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto: "On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts"J.Applied Probability. 35. 184-206 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsubara: "Stationary preserving ideals over Pk λ"J.Math.Soc.Japan. 55. 827-635 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara, M.Kubo: "The asymptotics of string matching probabilities for Gaussian random sequences"Nagoya Math.J.. 166. 39-54 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara: "Information transmission over Gaussian Channels with feedback"Proc Third Asian-European Workshop on Inform. Theory. 53-56 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara, Lin Gui Xin: "Error exponents for discrete-time white Gaussian channel with feedback"Proc. Meijo Winter Schoo on Quantum Inform. and Complexity. (To appear). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto, M.Yor: "Interpretation via Brownian motion of some independent properties between GIG and gamma variables"Stat.Prob.Lett.. 61. 253-259 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] H.Matsumoto: "On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts"J. Applied Probability. 35. 184-206 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsubara: "Stationary preserving ideals over Pk λ"J.Math.Soc. Japan. 55. 827-635 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] S.Ihara, Lin Gui Xin: "Error exponents for discrete-time white Gaussian channel with feedback"Proc.Meijo Winter School on Quantum Inform.and Complexity. (To appear). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Ihara: "Information transmission over Gaussian channels with feedback"Proc.Third Asian-European Workshop on Inform.Theory. 53-56 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 久保仁, 井原俊輔: "定常無記憶情報源の有歪み符号化における信頼性関数"第26回情報理論とその応用シンポジウム. 149-152 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Matsumoto, M.Yor: "Interpretation via Brownian motion of some independence properties between GIG and gamma variables"Stat.Prob.Lett.. 61. 253-259 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Matsumoto: "On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts"J.Applied Probability. 35. 184-206 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Matsubara: "Stationary preserving ideals over Pk λ"J.Math.Soc.Japan. 55. 827-835 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Ihara, M.Kubo: "The asymptotics of string matching probabilities for Caussian random sequences"Nagoya Mathematical Journal. 166. 39-54 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Ihara: "Error exponents of codings for stationary Gaussian channels"Proc.Intern.Couf.Quantum Information. (To appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Matsumoto, S.Taniguchi: "Wiener functionals of second order and their Levy measures"Electr.Journal of Probability. 7・14. 1-30 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Matsumoto, M.Yor: "Interpretation via Brownian motion of some independence properties between GIG and gamma variables"Stat.Prob.Lett. 61. 253-259 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Matsubara: "Stronger ideals over Pκλ"Fundamenta Mathematicae. 174・1. 229-238 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Matsubara: "Stationary preserving ideals over Pκλ"Journal of Math.Soc.Japan. (To appear). (2003)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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