Linear-Equation Ordered-Statistics Decoding

Abstract

In this paper, we propose a new linear-equation ordered-statistics decoding (LE-OSD). Unlike the OSD, LE-OSD uses high reliable parity bits rather than information bits to recover the codeword estimates, which is equivalent to solving a system of linear equations (SLE). Only test error patterns (TEPs) that create feasible SLEs, referred to as the valid TEPs, are used to obtain different codeword estimates. We introduce several constraints on the Hamming