基于杨辉三角结构的QC-LDPC码构造

Construction of QC-LDPC codes based on Yang Hui triangle

针对准循环低密度奇偶校验(QC-LDPC)码中准循环基矩阵的移位系数确定问题,提出基于杨辉三角结构的确定方法。该方法构造的校验矩阵不含四环,移位系数由简单的数学表达式确定,编码复杂度与码长呈线性关系,节省存储空间,对码长和码率参数的设计具有较好的灵活性。仿真结果表明:在加性高斯白噪声信道和BP译码算法下,该方法构造的码字在误比特率为10-4时,信噪比优于随机LDPC码接近0.3 dB,在误比特率为10-6时优于DVB-S2标准的LDPC码0.2 dB,并可以获得与IEEE 802.16e码相一致的性能。同时表明合理的选择循环移位矩阵的尺寸,可以改善码字的误比特率性能。

For the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the quasi-cyclic low-density parity-check, a method was presented based on Yang Hui triangle to compute the cyclic shift coefficients. By this method, cyclic shift coefficients could be expressed in simple analytic expressions, and cycles of length four in parity matrix were eliminated. The parity matrix is quasi-cyclic to save required memory and is prone to coding and decoding, and has high flexibility with respect to the design of code length and rate. Over an additive white Gauss noise channel and under the BP decoding algorithm, simulations show that the SNR of the QC-LDPC codes with the proposed algorithm is better than random codes close to 0.3 dB at the BER performance of 10-4 and better than the LDPC codes in DVB-S2 0.2 dB at the BER performance of 10^-6. Moreover, the BER performance of the new codes is no less than the LDPC codes in IEEE 802.16e under the same conditions. Furthermore, the simulation result also indicates that by making a reasonable choice of the size of the cyclic shift matrix, the BER performance of the codeword can be improved.