MATLAB: Does it take longer to compute the convolution in GF(2) when compared to an equivalent approach using FFT/IFFT

Question

I am trying to generate a lot of bits and code them using CRC-32. When comparing two approaches, convolution and FFT/IFFT, the answers are the same. However, the convolution approach takes significantly longer that the FFT/IFFT approach. For example, to generate 100 bits, convolution takes about 4 seconds while the FFT/IFFT takes only about 0.2 seconds. I would like to know the reason for the different computation times.

Answer 1

This is expected behavior. If implemented correctly, both approaches are equivalent. However, the FFT approach requires less mathematical operations and is therefore faster, especially for large data sets.