COSC 6365 – Spring 2008 – Lecture # 26 - 2 : Fast Fourier Transforms – II 3 Time Memory

The FFT performs butterfly computations on pairs of data elements that differ in a single bit. The computations start from the most significant bit in the index space and proceeds monotonically to the least significant bit. In a binary cube, adjacent nodes differ in a single bit in their addresses. Thus, mapping data to nodes by a binary encoding of the indices is suitable for the FFT. We assume such a mapping in the discussion below. In [4] we show that the same communication complexity can indeed be obtained for binary–reflected Gray code data encodings, even though the elements in a butterfly computation are no longer nearest neighbors, but at a distance of two apart. For Gray coded data, a code conversion is performed concurrently with the butterfly network emulation without an increase in the communication cost.