Blind Recognition of BCH Code Based on Galois Field Fourier Transform

In this paper, a new method for blind recognition of BCH code from an intercepted sequence of noise affected codewords is proposed. The proposed method recovers the parameters of a BCH code by finding the roots of it's generator polynomial. Firstly, the Galois Field Fourier Transfbrm (GFFT) operation is carried out for each sequence of an estimated length. Then, find the positions of common zero spectral components of all sequences' GFFT. If such positions exist, the corresponding estimated length is the code length and the roots of the underlying generator polynomial are found. Furthermore, the theoretical analysis of the proposed method is given in detail and an optimal threshold is derived to minimize the summation of the false alarm and miss detection probability for distinguishing the root and non-root of the generator polynomial. Simulation results show that the proposed method outperforms the previous ones.