Fault-tolerant 2D Fourier transform with checksum encoding

Space-based applications increasingly require more computational power to process large volumes of data and alleviate the downlink bottleneck. In addressing these demands, commercial-off-the-shelf (COTS) systems can serve a vital role in achieving performance requirements. However, these technologies are susceptible to radiation effects in the harsh environment of space. In order to effectively exploit high-performance COTS systems in future spacecraft, proper care must be taken with hardware and software architectures and algorithms that avoid or overcome the data errors that can lead to erroneous results. One of the more common kernels in space-based applications is the 2D fast Fourier transform (FFT). Many papers have investigated fault-tolerant FFT, but no algorithm has been devised that would allow for error correction without re-computation from original data. In this paper, we present a new method of applying algorithm-based fault tolerance (ABFT) concepts to the 2D-FFT that will not only allow for error detection but also error correction within memory-constrained systems as well as ensure coherence of the data after the computation. To further improve reliability of this ABFT approach, we propose use of a checksum encoding scheme that addresses issues related to numerical precision and overflow. The performance of the fault-tolerant 2D-FFT will be presented and featured as part of a dependable range Doppler processor, which is a subcomponent of synthetic-aperture radar algorithms. This work is supported by the Dependable Multiprocessor project at Honeywell and the University of Florida, one of the experiments in the Space Technology 8 (ST-8) mission of NASA's New Millennium Program.(12).