基于二维优化的QC-LDPC码构造方法

Construction of QC-LDPC codes based on two-dimentional optimization

研究了基于置换阵的QC-LDPC码圈长分布、ACE分布与对应的基矩阵结构之间的关系.在此基础上,提出在PEG构造框架下,联合优化校验矩阵圈长分布和ACE分布的QC-LDPC码构造方案.该构造方法不是单纯的以消除短圈或增加圈的ACE为目的,而是通过对圈长和ACE设定一个合理的约束关系,将ACE小的短圈尽量排除.由于基矩阵维数较少,新构造方法能够以较低的复杂度优化得到自适应多个扩张系数的基矩阵,从而得到一族不同码长的QC-LDPC码.仿真结果表明,在相同码率和节点度分布的条件下,新构造方法得到的一系列不同长度的码字,在BP算法下的性能都要优于IEEE802.16e中对应的QC-LDPC码字.

Several important relations are studied between the girth condition and the ACE （ approximated cycle extrinsic message degree） spectrum of the QC-LDPC （quasi-cyclic low-density parity- check） codes, where the PCM（ parity-check matrices） are defined by the base-matrix and expanded by the cyclic permutation matrices. According to this structure of PCM, a new algorithm for con- structing QC-LDPC codes is proposed, which follows the framework of PEG（ progress edge growth） algorithm and aims to jointly optimize girth condition and ACE spectrum of LDPC codes. In the pro- posed algorithm, not only the cycles with short lengths but also the cycles with small ACE values are reduced as far as possible, by setting a reasonable constraint relation to cycle lengths and ACE values. Due to the small dimension of base matrix, our construction can optimize an expansion factors adaptation base-matrix with low complexity and thus a class of QC-LDPC codes with different lengths is obtained. Simulation results show that the LDPC codes constructed by the proposed methodology outperform the QC-LDPC code adopted by IEEE 802. 16e with same code length, code rate and degree distribution.