Multiplier-Free Implementation of Galois Field Fourier Transform on a FPGA

A novel approach to implementing Galois field Fourier transform (GFT) is proposed that completely eliminates the need for any finite field multipliers by transforming the symbols from a vector representation to a power representation. The proposed method is suitable for implementing GFTs of prime and nonprime lengths on modern FPGAs that have a large amount of on-chip distributed embedded memory. For GFT of length 255 that is widely used in many applications, the proposed memory-based implementation exhibits 25% improvement in latency, 27% improvement in throughput, and 56% reduction in power consumption compared to a finite field multiplier-based implementation.