基于GFFT的LFSR序列生成多项式估计方法

Generator polynomial estimation of LFSR sequence based on GFFT

针对线性反馈移位寄存器(LFSR)序列生成多项式的估计问题,提出了一种基于LFSR序列有限域傅里叶变换(GFFT)的估计方法。首先证明了LFSR序列GFFT的非零点与LFSR序列生成多项式的零点之间的对应关系,进而利用该性质实现LFSR序列生成多项式的快速估计,并给出了算法在误码环境下的改进方法。仿真实验验证了算法的有效性,并对算法的计算复杂度进行了理论分析。和已有算法相比较,本文提出的算法具有更高的计算效率。

The problem addressed here is generator polynomial estimation of linear feedback shift register （LFSR） sequence. An algorithm based on the Galois field Fourier transform （GFFT） was proposed. The relationship between non-zero points in GFFT of LFSR sequence and zero points in generator polynomial of LFSR sequence was illustrated firstly. Then the generator polynomial of LFSR sequence was fast estimated based on that property, and the improved method in noisy environment was proposed at last. Validity of the algorithm is verified by the simulation resuits, and the computational load is illustrated. The computational efficiency of the proposed algorithm is higher than that of the existing algorithms.