Blind Recognition of Reed-Solomon Codes Based on Galois Field Fourier Transform and Reliability Verification

The Galois field Fourier transform (GFFT) method has been widely applied in the blind recognition of Reed-Solomon (RS) codes in recent years. However, as the code length increases, the computational complexity increases rapidly. Also, blind recognition in a poor channel environment remains challenging. To solve the above challenges, a blind recognition algorithm is proposed based on GFFT and reliability verification (RV). Low-complexity GFFT (LC-GFFT) is proposed to calculate the shortened spectrums, reducing the computational complexity and improving the correct codeword utilization rate (CUR). Next, the criteria for parameter estimation (PE) are given. The RV module is designed to verify the correctness of the estimated parameters. The simulations demonstrate that our algorithm can recognize RS(15, 11, 2, 19) and RS(31, 15, 8, 37) with over 95% correct rate when SNR is above 0.8dB and 2.5dB, achieving at least 7dB of signal-to-noise (SNR) defined gain over the existing algorithms. Moreover, the recognition time of our method is reduced by 74.8% compared to that of the GFFT-based method for RS(31, 15, 8, 37) when
$N = 1 \times 10^{5}$
.