Hamming Distance Distribution of the 0-reprocessing Estimate of the Ordered Statistic Decoder

In this paper, we derive the distribution of the Hamming distance at 0-reprocessing of the ordered statistics decoding (OSD). With the assumption of decoding a random linear block code, we first find the distribution of the number of errors in any partition of the ordered channel output sequence. Then the distribution of the Hamming distance after 0-reprocessing is derived by a mixture model of two random variables. Based on the proposed statistical approach, we outline the design of high-efficiency OSD algorithm. Simulation and numerical results show that our proposed statistical approaches accurately describe the Hamming distance distributions in OSD decoding process.

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