Reduced complexity ordered statistics decoding algorithm for MDS codes

The authors propose and analyze a reduced complexity ordered statistics decoding algorithm for maximum-distance separable (MDS) codes. The proposed algorithm provides a high degree of flexibility in the maximum number of candidate code words tested by the algorithm which yields different trade-offs between complexity and performance between orders of reprocessing. An upper bound to the error probability is calculated by extending the method proposed by D. Agrawal and A.Vardy (IEEE Trans. Inf. Theory, vol.46, p.60-83, 2000) for generalized-minimum-distance decoding. We present an application to singly-extended Reed-Solomon codes over GF(16) in a 128-dimensional multilevel coded modulation scheme that approaches the sphere lower bound within about 0.5 dB for a word error rate of 10^-4 with manageable decoding complexity.