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A Decoding Approach to Reed-Solomon Codes from Their Definition

  • Identification data

    Identifier: imarina:5132042
    Authors:
    Bras-Amorós M
    Abstract:
    Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple and it is difficult to fit them in introductory courses for undergraduates. We introduce a new decoding approach, in a self-contained presentation, which we think may be appropriate for introducing error correction of Reed-Solomon codes to nonexperts. In particular, we interpret Reed-Solomon codes by means of the degree of the interpolation polynomial of the code words and from this derive a decoding algorithm. Compared to the classical algorithms, our algorithm appears to arise more naturally from definitions and to be easier to understand. It is related to the Peterson-Gorenstein-Zierler algorithm (see [10 Gorenstein, D., Zierler, N. (1961). A class of error-correcting codes in pm symbols. J. Soc. Indust. Appl. Math. 9: 207-214. [Google Scholar]] and [20 Peterson, W. W. (1960). Encoding and error-correction procedures for the Bose-Chaudhuri codes.
  • Others:

    Author, as appears in the article.: Bras-Amorós M
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Bras Amoros, Maria
    Abstract: Because of their importance in applications and their quite simple definition, Reed-Solomon codes can be explained in any introductory course on coding theory. However, decoding algorithms for Reed-Solomon codes are far from being simple and it is difficult to fit them in introductory courses for undergraduates. We introduce a new decoding approach, in a self-contained presentation, which we think may be appropriate for introducing error correction of Reed-Solomon codes to nonexperts. In particular, we interpret Reed-Solomon codes by means of the degree of the interpolation polynomial of the code words and from this derive a decoding algorithm. Compared to the classical algorithms, our algorithm appears to arise more naturally from definitions and to be easier to understand. It is related to the Peterson-Gorenstein-Zierler algorithm (see [10 Gorenstein, D., Zierler, N. (1961). A class of error-correcting codes in pm symbols. J. Soc. Indust. Appl. Math. 9: 207-214. [Google Scholar]] and [20 Peterson, W. W. (1960). Encoding and error-correction procedures for the Bose-Chaudhuri codes.
    Thematic Areas: Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ciência da computação
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: maria.bras@urv.cat
    Author identifier: 0000-0002-3481-004X
    Record's date: 2024-09-07
    Papper version: info:eu-repo/semantics/acceptedVersion
    Link to the original source: https://www.tandfonline.com/doi/abs/10.1080/00029890.2018.1420333?journalCode=uamm20
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: American Mathematical Monthly. 125 (4): 320-338
    APA: Bras-Amorós M (2018). A Decoding Approach to Reed-Solomon Codes from Their Definition. American Mathematical Monthly, 125(4), 320-338. DOI: 10.1080/00029890.2018.1420333
    Article's DOI: 10.1080/00029890.2018.1420333
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2018
    Publication Type: Journal Publications
  • Keywords:

    Mathematics,Mathematics (Miscellaneous)
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    Matemática / probabilidade e estatística
    General mathematics
    Ciência da computação
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