Why does it take longer to compute the convolution in GF(2) when compared to an equivalent approach using FFT/IFFT?

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MathWorks Support Team
回答： Tasos Giannoulis 2017-1-25
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.

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MathWorks Support Team
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.

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Tasos Giannoulis
Tasos Giannoulis 2017-1-25
While it is hard to give a precise answer without looking at the exact code that you are comparing, a possible explanation is that some MATLAB functions (e.g., FFT) may be particularly optimized and exploit multi-threading, while some other function do not. If you are using GFCONV, the implementation is in C++ but no multi-threading is exploited there.

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