针对部分QC-LDPC(准循环低密度奇偶校验)码存在秩亏的问题，研究了一种满秩QC-LDPC码的构造方法，这种方法在降低编码复杂度的同时，还减少了短环数量。针对BP(置信传播)译码算法复杂度高的问题，提出了一种改进的BP译码算法，选择变量节点对数似然比值判决门限T=5.3和校验节点选择的边数q=3，在不同强度弱湍流条件下还能在一定程度上改善译码性能。研究表明，文章提出的LDPC码构造方法和译码算法在大气激光通信中具有一定的应用前景。

In this paper, we study a method for constructing a full-rank Quasi-Cyclic Low Density Parity Check (QC-LDPC) code, which can reduce encoding complexity and improve the performance of Bite Error Rate (BER) while reducing the number of short cycles. Furthermore, we present an improved Belief Propagation (BP) decoding algorithm, in which by selecting the variables node logarithmic likelihood ratio decision threshold T=5.3 and the number of parity node edges q=3, we can improve the decoding performance to a certain extent under the conditions of weak turbulences with different intensity. Our studies show the construction method for LDPC code and the improved decoding algorithm presented in this paper have broad prospects in atmospheric laser communications.