Partition decoding for reed-solomon codes based on bit reliability

This study presents a partition decoding algorithm for an (mN mK) binary image of an (N K) Reed Solomon code over GF(2m). A permutation is performed on a binary generator matrix of an RS code and a received vector, both of which are then partitioned into two submatrices and two subvectors. The first subvector of length N(m-1) associate with the first submatrix and the second subvector with the least subvector reliability value relates to the second submatrix. An MLD based on the first submatrix or a subfield subcode BCH generator matrix is employed to decode these two submatrices one after another. A codeword is finally outputted after performing the inverse permutation on a concatenation of code vectors decoded from these two decoding. Simulation results show that under a constraint of decoding complexity, a solution to decode binary images of long RS codes could be proposed partition decoding, which provides superior performance to GMD decoding with much lower complexity than the MLD.