Step-by-step error/erasure decoding reed-solomon codes

Abstract

A step-by-step error/erasure decoding algorithm for Reed-Solomon codes is presented. Compared with the standard algebraic decoding, this step-by-step error/erasure decoding algorithm does not need to find the coefficients of the error location polynomial, to search the error locators, and to calculate the error evaluator and error/erasure polynomials for obtaining the error and erasure values. This algorithm can detect whether each received code symbol is an error or erasure location or not and then directly find the corresponding error or erasure value in the manner of symbol-by-symbol.