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Geometrical decoding algorithm and the correcting limit of high-dimensional hypercubic ring code: correction ability at BER of 10–1 to 10–2.

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Title: Geometrical decoding algorithm and the correcting limit of high-dimensional hypercubic ring code: correction ability at BER of 10–1 to 10–2.
Authors: Kuroda, Shinichi1, Yamaguchi, Eisaku1, Takumi, Ichi1, Hata, Masayasu1
Source: Electronics & Communications in Japan, Part 3: Fundamental Electronic Science. May2001, Vol. 84 Issue 5, p75-85. 11p.
Subject Terms: *ERROR-correcting codes, *INFORMATION theory, *CODING theory, *ALGORITHMS, *MOBILE communication systems, *DATA transmission systems
Abstract: In this paper, a new decoding algorithm is proposed in which high-dimensional coding is done in a parity check code (high-dimensional ring code). The decoding method for the previously reported ring code has a complex correcting algorithm and requires much calculation time. We have focused on the point that a high-dimensional ring code can be divided into a number of two-dimensional ring codes, and by repeating the error correction of two-dimensional ring codes that requires small computation, we can perform error correction of high-dimensional ring codes. This decoding algorithm has a correction ability similar to the conventional decoding algorithms but with less computation. Moreover, when the error rate is high, random error and burst errors are mixed and an error correcting code is needed. However, since the decoding algorithm of the proposed code has a provision for dimensional division and the error generated on the transmitted block can be uniformly distributed on each two-dimensional plane, the error on the channel in the two-dimensional plane becomes random and error correction can be done efficiently. Moreover, if analysis or simulation increases the number of dimensions, then the correction ability is increased and the limit of the correction ability is determined from the size m of the code. The performance of convolutional codes and Reed Solomon codes is compared and it is shown that the ring code has high processing gain of error correction and that if the threshold point of correction lies in the high-error-rate region, then the decoding error rate is small and this code can be applied to high-error-rate correction. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(5): 75–85, 2001 [ABSTRACT FROM AUTHOR]
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  Label: Title
  Group: Ti
  Data: Geometrical decoding algorithm and the correcting limit of high-dimensional hypercubic ring code: correction ability at BER of 10<superscript>–1</superscript> to 10<superscript>–2</superscript>.
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  Data: <searchLink fieldCode="AR" term="%22Kuroda%2C+Shinichi%22">Kuroda, Shinichi</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Yamaguchi%2C+Eisaku%22">Yamaguchi, Eisaku</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Takumi%2C+Ichi%22">Takumi, Ichi</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Hata%2C+Masayasu%22">Hata, Masayasu</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Electronics+%26+Communications+in+Japan%2C+Part+3%3A+Fundamental+Electronic+Science%22">Electronics & Communications in Japan, Part 3: Fundamental Electronic Science</searchLink>. May2001, Vol. 84 Issue 5, p75-85. 11p.
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: *<searchLink fieldCode="DE" term="%22ERROR-correcting+codes%22">ERROR-correcting codes</searchLink><br />*<searchLink fieldCode="DE" term="%22INFORMATION+theory%22">INFORMATION theory</searchLink><br />*<searchLink fieldCode="DE" term="%22CODING+theory%22">CODING theory</searchLink><br />*<searchLink fieldCode="DE" term="%22ALGORITHMS%22">ALGORITHMS</searchLink><br />*<searchLink fieldCode="DE" term="%22MOBILE+communication+systems%22">MOBILE communication systems</searchLink><br />*<searchLink fieldCode="DE" term="%22DATA+transmission+systems%22">DATA transmission systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, a new decoding algorithm is proposed in which high-dimensional coding is done in a parity check code (high-dimensional ring code). The decoding method for the previously reported ring code has a complex correcting algorithm and requires much calculation time. We have focused on the point that a high-dimensional ring code can be divided into a number of two-dimensional ring codes, and by repeating the error correction of two-dimensional ring codes that requires small computation, we can perform error correction of high-dimensional ring codes. This decoding algorithm has a correction ability similar to the conventional decoding algorithms but with less computation. Moreover, when the error rate is high, random error and burst errors are mixed and an error correcting code is needed. However, since the decoding algorithm of the proposed code has a provision for dimensional division and the error generated on the transmitted block can be uniformly distributed on each two-dimensional plane, the error on the channel in the two-dimensional plane becomes random and error correction can be done efficiently. Moreover, if analysis or simulation increases the number of dimensions, then the correction ability is increased and the limit of the correction ability is determined from the size m of the code. The performance of convolutional codes and Reed Solomon codes is compared and it is shown that the ring code has high processing gain of error correction and that if the threshold point of correction lies in the high-error-rate region, then the decoding error rate is small and this code can be applied to high-error-rate correction. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(5): 75–85, 2001 [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1002/1520-6440(200105)84:5<75::AID-ECJC8>3.0.CO;2-G
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 75
    Subjects:
      – SubjectFull: ERROR-correcting codes
        Type: general
      – SubjectFull: INFORMATION theory
        Type: general
      – SubjectFull: CODING theory
        Type: general
      – SubjectFull: ALGORITHMS
        Type: general
      – SubjectFull: MOBILE communication systems
        Type: general
      – SubjectFull: DATA transmission systems
        Type: general
    Titles:
      – TitleFull: Geometrical decoding algorithm and the correcting limit of high-dimensional hypercubic ring code: correction ability at BER of 10–1 to 10–2.
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Kuroda, Shinichi
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            NameFull: Yamaguchi, Eisaku
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            NameFull: Takumi, Ichi
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            NameFull: Hata, Masayasu
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          Dates:
            – D: 01
              M: 05
              Text: May2001
              Type: published
              Y: 2001
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              Value: 10420967
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            – Type: volume
              Value: 84
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: Electronics & Communications in Japan, Part 3: Fundamental Electronic Science
              Type: main
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