High speed decoding of Reed-Solomon codes

摘要

This specification covers a simplified and high speed decoding scheme for Reed-Solomon codes capable of correcting up to three symbol errors in code words made up of k data and n-k check symbols where each symbol consists of m binary bits of information. In such a code the error location polynomial sigma (x) = xe + sigma 1xe-1 . . . . sigma e where e equals the number of symbol errors and the coefficient of sigma (x) are related to the error syndromes Si by the equation Si+e + sigma 1Si+e-1 +. . . . + sigma e-1 Si+1 + sigma eSi = 0.