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Approach to Some Open Problems about Shannon's Channel Coding Theorem

Research Project

Project/Area Number 16560348
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, Faculty of Computer and Information Sciences, Professor, 情報科学部, 教授 (70211456)

Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
KeywordsMaximum Distance Separable Codes / Generalized Reed-Solomon Codes / Hamming Weight Distribution / Probability of an Undetected Error / Complete Weight Distribution / Asymptotic Distance Ratio / Reed-Solomon符号 / 重み分布
Research Abstract

There are four in points of our research results as follows
1.Let A (w, w_<inf>) be the number of codewords of both weight w_<inf> in the information symbols and weight w_<che> in the check symbols for the Hamming weight w= w_<inf>+w_<che>, then we got the explicit A (w, w_<inf>) with a recurrence formula.
2.By utilizing certain characteristic structure of the Hamming weight distribution of maximum distance separable codes and proposition of systematic codewords, we can get weight enumerators to calculate upper and lower bounds on the probability of an undetected error for binary expansions of generalized Reed-Solomon codes. To show the effectiveness of these weight enumerators, the numerical value is calculated in this report. That is, concrete parameters that can calculate the weight distribution of binary expansion of Reed-Solomon code by all searches of the computer are given, and the true value of the probability of an undetected error for this code is calculated. Moreover, for give … More n concrete parameters of Reed-Solomon codes, the average probability of an undetected error over the set of binary expansions of generalized Reed-Solomon codes is calculated by using the average weight distribution for a class of generalized Reed-Solomon codes. By comparing these values with values of upper and lower bound on the probability of an undetected error for binary expansions of generalized Reed-Solomon codes calculated from those weight enumerators, the effectiveness of those weight enumerators is shown.
3.By utilizing certain characteristic structure of the Hamming weight distribution of maximum distance separable codes and proposition of systematic codewords, we can get weight enumerators to calculate upper and lower bounds on the probability of an undetected error for a class of binary expansions of concatenated codes with generalized Reed-Solomon outer codes.
4.By using a feature structure of the Justesen code, the weight distributions for the families of the Justesen codes having low code rates are explicitly given by Kolev and Kohnosu--Tokiwa. However, an asymptotic evaluation to these families is not given in those papers. Then, 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. Comparing with the lower bound on the asymptotic distance ratio for Justesen codes, the location of the asymptotic ability that those families have is clarified. Less

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (2 results)

All 2004

All Journal Article (2 results)

  • [Journal Article] 外部符号にリードソロモン符号をもつ2値展開された連接符号の見逃し誤り確率の近似計算について2004

    • Author(s)
      西島利尚
    • Journal Title

      電子情報通信学会論文誌A Vol. J87-A No. 2

      Pages: 319-328

    • NAID

      110003311768

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] On a Good Approximation to the Probability of an Undetected Error for Binary Expansions of Concatenated Codes with Reed-Solomon Outer Codes2004

    • Author(s)
      Toshihisa Nishijima
    • Journal Title

      The transactions of The Institute of Electronics, Information and Communication Engineers A Vol.87-A No.2

      Pages: 319-328

    • NAID

      110003311768

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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