利用域间映射的多元QC-LDPC码构造

Construction of Q-ary QC-LDPC Codes with Galois Filed Mapping

通过定义有限域间的映射关系,提出了一种低复杂度的多元准循环奇偶校验码(QC-LDPC)的构造方法。利用这种方法可将较高阶数有限域的校验矩阵映射到指定的较低有限域上,且能保持原矩阵的结构性与稀疏特性。所构造的多元LDPC码不仅具有较低的译码复杂度且具有准循环特性,在硬件上也易于用移位寄存器实现。在高斯白噪声(AWGN)信道下的仿真结果表明,所构造的多元QC-LDPC码具有良好的编译码性能。当误码率为10^(-6)时,码率为0.765的QC-LDPC码在目标域GF(8)上能获得0.2 d B的性能增益。

An approach to construct Q-ary quasi-cyclic（ QC） low density parity check（ LDPC） codes with low decoding complexity is presented by defining a mapping relationship over Galois field. With this meth-od,the parity check matrix over a higher order Galois field can be mapped to a designated Galois field, which can keep its structural property and density degree. Codes constructed by this method have low deco-ding complexity and quasi-cyclic characteristic,which can be easily implemented by shift registers. Simula-tion results show that the constructed codes have good performance over additive white Gaussian noise （ AWGN） channel. Compared with the original codes,QC-LDPC codes with rate 0. 765 at targeted field GF （8） can achieve a performance gain about 0. 2 dB around 10^-6 bit error rate（BER）.