里德-所罗门码的纠错概率

Proceedings International Conference on Information Technology: Coding and Computing (Cat. No.PR00540) Pub Date : 2000-03-27 DOI:10.1109/ITCC.2000.844260

I. Sofair

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引用次数: 7

摘要

当错误数量超过附加里德-所罗门字符数量的一半时，解码器无法将错误消息纠正为原始未受污染的版本。在大多数情况下，Reed-Solomon算法可以通过内置过滤器检测到过量错误的存在。然而，在少数情况下，消息可能被更正为不同的码字，在这种情况下，它被称为错误更正。利用最大2/sup m/-个字符集(GF(2/sup m/))，给出了给定e个错误的情况下，2/sup m/>n的n字符信息的t-纠错里德-所罗门码纠错概率的一般表达式。

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Probability of miscorrection for Reed-Solomon codes

The decoder fails to correct an erroneous message to its original untainted version when the number of errors exceeds half the number of appended Reed-Solomon characters. In most cases, the Reed-Solomon algorithm can detect the presence of an excess of errors through built-in filters. However, in a few cases, the message may be corrected to a different code word in which case it is said to be miscorrected. This paper derives a general expression for the probability of miscorrection of an n-character message with a t-error correcting Reed-Solomon code that utilizes a maximum 2/sup m/-character set (GF(2/sup m/)), where 2/sup m/>n, given e errors.

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Proceedings International Conference on Information Technology: Coding and Computing (Cat. No.PR00540)

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