Efficient frequency domain decoding of binary BCH codes based on prime-factor FFT

By introducing the ideas of reducing computation complexity in the fast Fourier transform (FFT) to decoding, a low complexity decoding of binary BCH codes is derived which transforms the determination of one-dimensional error word into two-dimensional matrix. For the case of double-error-correcting binary BCH codes, the frequency domain decoding based on prime-factor FFT (in short, PF-FDD) was designed. Compared with the conventional frequency domain decoding algorithm, PF-FDD has the advantages of lower decoding complexity and faster decoding speed at the expense of increasing storage memory. When compared with the ordinary look-up table decoding scheme, the error patterns to store are decreased greatly. Hence, PF-FDD achieves a better tradeoff between decoding complexity and hardware complexity. The proposed low complexity decoding scheme is suitable for binary BCH codes whose block length has prime factors and error correcting capacity is relatively small, and is expected to apply to soft-decision decoding.