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Fault tolerance in computing, compressing, and transmitting FFT data

Remote-sensing applications often calculate the discrete Fourier transform of sampled data and then compress and encode it for transmission to a destination. However, all these operations are executed on computing resources potentially affected by failures. Methods are presented for integrating various fault detection capabilities throughout the data flow path so that the momentary failure of any subsystem will not allow contaminated data to go undetected. New techniques for protecting complete source coding schemes are exemplified by examining a lossy compression system that truncates fast Fourier transform (FFT) coefficients to zero, then compresses the data further by using lossless arithmetic coding. Novel methods protect arithmetic coding computations by internal algorithm checks. The arithmetic encoding and decoding operations and the transmission path are further protected by inserting sparse parity symbols dictated by a high-rate convolutional symbol-based code. This powerful approach introduces limited redundancy at the beginning of the system but performs detection at later stages. While the parity symbols degrade efficiency slightly, the overall compression gain is significant because of the run-length coding. Well-known fault tolerance measures for FFT algorithms are extended to detect errors in the lossy truncation operations, maintaining end-to-end protection. Simulations verify that all single subsystem errors are detected and the overhead costs are reasonable.