Design of BP-Based Decoding for Short LDPC Codes Using MMSE Criterion

By using the minimum mean square error (MMSE) criterion, we show the design of the scaled and offset belief propagation (BP)-based decoding for short low-density parity-check (LDPC) codes on the channels of additive white Gaussian noise (AWGN) and uncorrelated flat Rayleigh fading with side information (SI). Based on the MMSE criterion, the detailed derivations and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (3,6) regular LDPC codes on the AWGN and Rayleigh fading channels demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance almost the same to, and even better than that of the BP algorithm.