基于矩阵分解的有限几何LDPC码的研究

Research of construction algorithm of finite geometry LDPC codes based on matrix decomposition

随机构造的LDPC（low density parity check codes）码长的增加,所需存储空间过大,编码复杂度过高.针对该问题,研究了具有代数结构的有限几何LDPC码.基于有限域几何空间的点和线来构造校验矩阵,并通过矩阵行列分解得到不同码率、码长的非规则QC-LDPC码.该类LDPC码是准循环码,其编码复杂度与码长成线性关系,对应的Tanner图没有4环存在.仿真结果表明：MSK调制、AWGN信道条件下,该类码与类似参数的随机码相比较,当信道误码率为10-6时,译码增益约为0.05～0.15dB.

With the growth of length, random LDPC （low density parity check） codes need large memory to storage the matrixes and have high encoding complexity. In this paper, in order to solve the problems, the algebraic methods based on finite geometry are researched. The parity check matrixes are constructed by the points and lines of finite geometries. The technique of matrix decomposition is used to get irregular QC-LDPC codes with various rates and code lengths. These codes are quasi-cyclic codes and can be encoded with low complexity with a linear relationship to code length. They also have Tanner graphs free of 4-cycles. The simulation results indicate： in the condition of MSK modulation and AWGN channel, these codes have decoding performance gains about 0.05 to 0.15dB when bit error rate is 10^-6 compared with random LDPC codes with similar parameters.