Due to high complexity of Belief Propagation(BP) algorithm, several kind of BP-based simplified decoding algorithms are analyzed. Based on the Minimum Mean Square Erro(MMSE) criterion, optimal design of the scaled BP-based and offset BP-based algorithms is discussed. The theoretical formulas and numerical calculations on the optimal factors for these two BP-based algorithms are provdied. The simualtion resutls for the (6,3)regualr LDPC codes of lengths 1008 on the weak atmospheric turbulence channel demonstrate that the scaeld BP-based and offset BP-based aglorithms with the proposed factors are better than Min-Sum Algorithm, and even can achieve the performance better than that of the BP algorithm,and have lower complexity compared with BP algortihm.