Some basic characteristics of Galois Field are analyzed. At the same time, some basic methods for constructing Quasi Cycle Low Density Parity Check (QC-LDPC) codes are presented. A method of constructing QC-LDPC codes based on Grouping of Galois Field's Extension Field can be realized. By grouping Galois Extension Field's linear independent elements, the QC-LDPC codes with different rates can be easily constructed. Simulation results show that under 10-5 BER, our method has almost the same performance as codes constructed based on dayan sequence, the latter has 0. 1 dB more gain than the former. Compared with codes constructed based on Fibonacci sequence, our method has 0. 8 dB more gain. Our method has 1 dB gain less than the method proposed by IEEE802. 16e standard. It still has large space to improve the method.%分析了伽罗华域的一些基本性质,同时,给出了准循环低密度奇偶校验码的基本构造思路与方法.在此基础之上,提出了基于伽罗华域扩域分组方法构造多码率QC-LDPC码的方法.通过对扩展域中线性独立的元素的分组,可以很容易地实现不同码率QC-LDPC码的构造.仿真显示,提出的方法在10-5误码率条件下,与基于大衍数列构造的QC-LDPC码性能接近,有0.1 dB的差距,但是,与基于斐波那契构造的QC-LDPC码相比,有0.8 dB的增益.与IEEE 802.16e构造的QC-LDPC码相比,提出的方法有1 dB的差距,还有很大的改进空间.
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