In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and order statistic decoding (OSD) algorithms. Specifically, a modified BP (mBP) algorithm is applied for a certain number of iterations prior to OSD to enhance the reliability of the received message, where an offset parameter is utilized in mBP to control the weight of the extrinsic information in message passing. By carefully selecting the offset parameter and the number of mBP iterations, the number of errors in the most reliable positions (MRPs) in OSD can be reduced, thereby significantly improving the overall decoding performance of error rate and complexity. Simulation results show that the proposed algorithm can approach the maximum-likelihood decoding (MLD) for short LDPC codes with only a slight increase in complexity compared to BP and a significant decrease compared to OSD. Specifically, the order-(m-1) decoding of the proposed algorithm can achieve the performance of the order-m OSD.

翻译：本文提出了一种通过精心结合置信传播（BP）译码与序贯统计译码（OSD）算法来实现短低密度奇偶校验（LDPC）码的高效译码算法。具体而言，在OSD之前应用改进的BP（mBP）算法进行一定次数的迭代，以增强接收消息的可靠性，其中mBP利用偏移参数控制消息传递中外信息权重。通过精心选择偏移参数和mBP迭代次数，可减少OSD中最可靠位置（MRP）的误码数量，从而显著提升整体误码率性能和降低复杂度。仿真结果表明，该算法在复杂度仅比BP略有增加且显著低于OSD的情况下，可逼近短LDPC码的最大似然译码（MLD）。具体而言，所提算法的(m-1)阶译码可实现m阶OSD的性能。