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2010 Fiscal Year Final Research Report

Shannon's channel coding problems from points of view of both information theory and algebraic coding theory

Research Project

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Project/Area Number 20560372
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Communication/Network engineering
Research InstitutionHosei University

Principal Investigator

NISHIJIMA Toshihisa  Hosei University, 情報科学部, 教授 (70211456)

Project Period (FY) 2008 – 2010
Keywords情報理論 / 符号理論
Research Abstract

It is well known that each bound of reliability function, asymptotic distance ratio, and the probability of undetected error for the ensemble of all binary linear block codes is given. Therefore we think that it is an important research to get each bound of those functions for an ensemble of some important subclasses of binary linear block codes in order to find a clue to a solution for some open problems in information theory or the theory of error correcting codes. (1) By using a feature structure of the Justesen code, the convergent points of the asymptotic distance ratio that those families have are specified on the basis of not a lower bound but minimum weights obtained from those weight distributions. (2) By utilizing certain characteristic structure of the Hamming weight distribution of maximum distance separable codes, we can get weight enumerators to compute an upper and a lower bound on the probability of an undetected error for binary expansions of generalized Reed-Solomon codes. Also, values of the average probability of an undetected error are computed by using the average weight distribution for an ensemble of binary expansions of all codewords of all Reed-Solomon codes for some given concrete code parameters. (3) We show some properties of the weight enumerators of all the codes over GF (2m) in Wozencraft's ensembles of randomly shifted codes

  • Research Products

    (10 results)

All 2010 2009 2008

All Journal Article (3 results) (of which Peer Reviewed: 3 results) Presentation (7 results)

  • [Journal Article] 2値に展開された連接符号の見逃し誤り確率の上界と下界について2009

    • Author(s)
      西島利尚
    • Journal Title

      電子情報通信学会論文誌 Vol.J92A No.1

      Pages: 48-54

    • Peer Reviewed
  • [Journal Article] Wozencraftのランダムシフト符号とその集合族が有する2元重み分布多項式に関するいくつかの性質2009

    • Author(s)
      鴻巣敏之、西島利尚、常盤欣一朗
    • Journal Title

      電子情報通信学会論文誌 Vol.J92A No.4

      Pages: 724-726

    • Peer Reviewed
  • [Journal Article] 低符号化比率のJustesen符号に対する漸近的距離比の収束点2008

    • Author(s)
      鴻巣敏之、西島利尚、常盤欣一朗
    • Journal Title

      電子情報通信学会論文誌 Vol.J91A No.5

      Pages: 587-590

    • Peer Reviewed
  • [Presentation] Upper bounds on the average probability of an undetected error for the ensemble of both product and concatenated codes2010

    • Author(s)
      西島利尚, 常盤欣一朗
    • Organizer
      The 2010 International Symposium on Information Theory and Its Applications(査読あり)
    • Place of Presentation
      台湾(台中市)
    • Year and Date
      20101017-20101020
  • [Presentation] 可変内部符号化された2元連接符号の集合族上に与えられる平均見逃し誤り確率の上界式について2009

    • Author(s)
      西島利尚、常盤欣一朗
    • Organizer
      電子情報通信学会技術研究報告(IT-2008-112 pp.453-457)
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-09-25
  • [Presentation] 連接符号の信頼度関数・漸近的距離比・見逃し誤り確率について2009

    • Author(s)
      西島利尚、常盤欣一朗
    • Organizer
      電子情報通信学会技術研究報告(IT-2009-31 pp.147-152)
    • Place of Presentation
      関西学院大学
    • Year and Date
      2009-07-24
  • [Presentation] 積符号の信頼度関数・漸近的距離比・見逃し誤り確率について2009

    • Author(s)
      西島利尚、常盤欣一朗
    • Organizer
      電子情報通信学会技術研究報告(IT-2008-112 pp.453-457)
    • Place of Presentation
      公立はこだて未来大学
    • Year and Date
      2009-03-10
  • [Presentation] 一般化リード-ソロモン符号の集合族における原始リード-ソロモン符号の特定2008

    • Author(s)
      西島利尚、常盤欣一朗、鴻巣敏之
    • Organizer
      第31回情報理論とその応用シンポジウム予稿集(pp.724-726)
    • Place of Presentation
      鬼怒川温泉あさやホテル
    • Year and Date
      2008-10-09
  • [Presentation] Wozencraftのランダムシフト符号とその集合族が有する2元重み分布多項式に関するいくつかの性質2008

    • Author(s)
      西島利尚、常盤欣一朗、鴻巣敏之
    • Organizer
      電子情報通信学会技術研究報告(IT-2008-35 pp.91-94)
    • Place of Presentation
      カルチャーリゾート・フェストーネ(沖縄県宜野湾市)
    • Year and Date
      2008-09-12
  • [Presentation] 原始リード-ソロモン符号の2元重み分布のクラス分けについて2008

    • Author(s)
      遠藤寿之、西島利尚、常盤欣一朗、鴻巣敏之
    • Organizer
      電子情報通信学会技術研究報告(IT-2008-36 pp.95-98)
    • Place of Presentation
      カルチャーリゾート・フェストーネ(沖縄県宜野湾市)
    • Year and Date
      2008-09-12

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Published: 2012-01-26   Modified: 2016-04-21  

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