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Introduction to Reed-Solomon Codes

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Reed-Solomon (R-S) codes are nonbinary codes; that is, we can describe them in terms of symbols rather than bits. Such codes can achieve very large minimum distances. When an R-S decoder corrects a symbol, it replaces the incorrect symbol with the correct one, whether the error was caused by one bit being corrupted or all of the bits being corrupted. Thus, if a symbol is wrong, it might as well be wrong in all of its bit positions. This gives R-S codes tremendous burst-noise advantages over binary codes. This article explores the mathematical details of how R-S encoders and decoders work, and provides numerical examples to illustrate their error performance.
This article is excerpted from Digital Communications: Fundamentals and Applications, Second Edition (Prentice-Hall, 2001, ISBN 0-13-084788-7).
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In 1960, Irving Reed and Gus Solomon published a paper in the Journal of the Society for Industrial and Applied Mathematics. This paper described a new class of error-correcting codes that are now called Reed-Solomon (R-S) codes. These codes have great power and utility, and are today found in many applications from compact disc players to deep-space applications. This article is an attempt to describe the paramount features of R-S codes and the fundamentals of how they work.

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