基于伽罗华域高斯列消元法的 RS 码盲识别

摘要

In order to solve the blind recognition problem of the high rate Reed Solomon(RS) codes,this paper presents a blind recognition method based on Galois Field columns Gaussian elimination. Firstly,code length and symbolic number are recognized by using the difference function of the matrix rank. Then the primitive polynomials corresponding to the number of symbol at this time are traversed. And the matrix is e-liminated with columns in Galois field. By using the difference of entropy,the primitive polynomial is identi-fied. Finally,as the code word polynomial roots are found,the continuous roots are the roots of the generator polynomial. Code length,the primitive polynomial and the generator polynomial are identified by the meth-od. The tedious process of Galois field Fourier transform is avoided. Simulation results show that the recog-nition probability is higher than 90% at an error code rate of 3×10-3 .%为解决高码率 RS(Reed Solomon)码盲识别问题，提出了一种基于伽罗华域高斯列消元法的RS 码盲识别方法。先利用矩阵秩的差值函数识别符号数及码长；再遍历此时符号数对应的本原多项式，对矩阵进行伽罗华域高斯列消元，并引入熵函数差值来识别本原多项式；最后求码字多项式的根，其中连续根即为生成多项式的根。该方法可以较好地识别 RS 码码长、生成多项式及本原多项式，并且避免了遍历符号数时多次进行伽罗华域傅里叶变换的繁琐过程。仿真结果表明，在误码率为3×10-3的情况下，对 RS 码的识别概率高于90%。