Abstract: In order to reduce the LDPC (Low-Density Parity-Cheek) complexity of decoding algorithm, studied
the LLR BP (Log-Likelihood Ratio Belief Propagation algorithm) and its simplified decoding algorithm, and an
improved algorithm based on NMS (Normalized Min Sum) algorithm is proposed; studied the Gamma-Gamma
distribution model and Gamma-Gamma distribution as the channel model are studied. The performance of LLR-
BP and its simplified algorithm under different turbulence intensities are compared with Matlab, the simulation
results show that both in the AWGN (Additive White Gaussian Noise) or different turbulence intensity Gamma-
Gamma channel, the improved algorithm has better performance in decoding algorithms in particular, the
performance advantages of the improved algorithm in strong turbulence is more obvious. The simulation results
show that the increase of the code length can improve the performance of the BER (Bit Error Rate).

Key words: low-density parity-cheek ( LDPC), min sum algorithm, normalized BP-based algorithm, Gamma-Gamma distribution, log-likelihood ratio belief propagation (LLR-BP)