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 by mBP, 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：本文通过谨慎结合置信传播（BP）译码与有序统计译码（OSD）算法，提出了一种适用于短低密度奇偶校验（LDPC）码的高效译码算法。具体而言，在OSD之前执行若干次迭代的改进型BP（mBP）算法，以增强接收信息的可靠性；其中，mBP利用偏移参数控制消息传递中外赋信息的权重。通过精心选择偏移参数与mBP迭代次数，mBP能够减少OSD中最可靠位置（MRPs）的误码数，从而显著提升整体的误码率性能和计算复杂度。仿真结果表明，所提算法能够逼近短LDPC码的最大似然译码（MLD），相比BP仅小幅增加复杂度，而相比OSD则显著降低复杂度。特别地，所提算法的阶-(m-1)译码能够实现阶-m OSD的性能。