  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.
