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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Bibliographic Details
Published in:The American mathematical monthly Vol. 125; no. 4; pp. 320 - 338
Main Author: Bras-Amorós, Maria
Format: Journal Article
Language:English
Published: Washington Taylor & Francis 21.04.2018
Taylor & Francis, Ltd
Taylor & Francis Ltd
Subjects:
Algorithms
Coding theory
Decoding
Error correction
Interpolation
Introductory Courses
Polynomials
Primary 12Y05
Secondary 94B35
ISSN:0002-9890, 1930-0972
Online Access:Get full text
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Summary: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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ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2018.1420333