Low-Complexity Parallel Syndrome Computation for BCH Decoders Based on Cyclotomic FFT

The long binary Bose-Chaudhuri-Hochquenghem (BCH) codes are widely used in communication and storage systems, and massive-parallel BCH decoders are expected to satisfy the requirement of high throughput. However, a large parallel degree leads to a significant increase in the hardware complexity of the syndrome computation (SC) module. Considering the similarities between SC and discrete Fourier transform (DFT), this paper proposes an advanced cyclotomic fast Fourier transform (CFFT) algorithm-aided SC architecture, which fully utilizes the property of characteristic-2 fields of binary BCH codes to reduce hardware complexity. The implementation results show that the proposed CFFT-aided architecture is desirable for long binary BCH codes with the error-correction capability less than 20. For (16383, 16271, 8) BCH code over GF(2
¹⁴
), the hardware overhead of a 128-parallel SC module is reduced by 16% compared to the state-of-the-art architecture.