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：本文通过精心结合置信传播译码与有序统计译码算法，提出了一种适用于短低密度奇偶校验码的高效译码算法。具体而言，在有序统计译码之前，采用改进的置信传播算法执行特定次数的迭代，以增强接收信息的可靠性，其中改进的置信传播算法通过引入偏移参数来控制消息传递中外赋信息的权重。通过合理选取偏移参数与改进的置信传播迭代次数，可降低有序统计译码中最可靠位置上的错误数量，从而显著提升误码率与复杂度方面的整体译码性能。仿真结果表明，所提算法能够逼近短低密度奇偶校验码的最大似然译码性能，其复杂度较置信传播算法仅有微小增加，而相比有序统计译码则显著降低。特别地，所提算法进行(m-1)阶译码时即可达到有序统计译码m阶译码的性能。