Probability of miscorrection for Reed-Solomon codes

Abstract

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.