A Decoding Approach to Reed-Solomon Codes from Their Definition
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 un...
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| Vydáno v: | The American mathematical monthly Ročník 125; číslo 4; s. 320 - 338 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Washington
Taylor & Francis
21.04.2018
Taylor & Francis, Ltd Taylor & Francis Ltd |
| Témata: | |
| ISSN: | 0002-9890, 1930-0972 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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
] and [
20
]). |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0002-9890 1930-0972 |
| DOI: | 10.1080/00029890.2018.1420333 |