A Revisit to Ordered Statistic Decoding: Distance Distribution and Decoding Rules
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This paper revisits the ordered statistic decoder (OSD) and provides a comprehensive analyses of OSD decoding by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimation to the received signals in the reprocessing stages of the OSD decoder. We prove that both the distributions of Hamming distance and weighted Hamming distance can be characterized as Gaussian mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that the distance distributions can be accurately described by our proposed statistical approaches. Based on these distributions, several decoding techniques, including sufficient and necessary conditions, are proposed for reducing the decoding complexity and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that proposed decoding techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.
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