Parallel 1D-FFT Computation on Constant-valence Multicomputers

This paper addresses the problem of monodimensional (1D) FFT parallel computation on constantvalence multicomputers, i.e. on parallel systems made up of processing elements (PEs) which do not share memory and are connected to a bounded number of neighbours. After a qualitative analysis of several possible partitionings of the DIT FFT algorithm, a decomposition is introduced that has good scalability properties and makes it possible to use sections of sequential code based on the most common 1D-FFT algorithms. If a computing architecture with indirect binary n-cube interconnection network is used, the proposed decomposition guarantees strictly local communications and therefore requires no through-routing support. These characteristics have a positive impact on software development and also on overall performance. Furthermore, thanks to a pipelined organization of the PEs, the resulting architecture has high potentialities for real-time signal processing. As these useful features are obtained at the `expense' of an uneven workload distribution, computing efficiency is relatively low but does not significantly change in a wide range of the number of processors. An implementation on a Transputer-based system is presented along with the performance results obtained. Finally a simple analytical model of the architecture is shown, that allows the values of the main performance parameters to be obtained as a function of the number of processors used and of the elementary response times of the first stage of PEs. key words : FFT; parallel processing; constant-valence multicomputers; transpute