  This paper revisits the ordered statistics decoding (OSD). It provides a
comprehensive analysis of the OSD algorithm by characterizing the statistical
properties, evolution and the distribution of the Hamming distance and weighted
Hamming distance from codeword estimates to the received sequence in the
reprocessing stages of the OSD algorithm. We prove that the Hamming distance
and weighted Hamming distance distributions can be characterized as mixture
models capturing the decoding error probability and code weight enumerator.
Simulation and numerical results show that our proposed statistical approaches
can accurately describe the distance distributions. Based on these
distributions and with the aim to reduce the decoding complexity, several
techniques, including stopping rules and discarding rules, are proposed, and
their decoding error performance and complexity are accordingly analyzed.
Simulation results for decoding various eBCH codes demonstrate that the
proposed techniques can significantly reduce the decoding complexity with a
negligible loss in the decoding error performance.
