Fast Blind Recognition of BCH Code Based on Spectral Analysis and Probability Statistics

Abstract

This letter presents a fast blind recognition method for Bose, Chaudhuri, and Hocquenghem (BCH) code from noisy intercepted bit-streams. This approach employs the fact that the t-error-correcting BCH code has 2t continuous roots, and the roots correspond with the zero spectral. Specifically, the Galois field Fourier transform is simplified (S-GFFT) by using the property of conjugate roots. Then, the distribution characteristics of continuous zero spectra are analyzed. If the continuous zero spectra satisfy the threshold condition which is derived by the probability of zero spectrum component, the corresponding estimated length is the code length, and the relevant positions correspond to the continuous roots of the generated polynomial. Finally, the generator polynomial can be reconstructed based on algebras theory. Compared to the existing solutions, the computational amount of S-GFFT at most accounts for 60% of GFFT, and the proposed scheme manages to recognize the code parameters without traversing the whole candidate datasets.