Fast fault-tolerant digital convolution using a polynomial residue number system

A fault-tolerant convolution algorithm that is an extension of residue-number-system fault-tolerance schemes applied to polynomial rings is described. The algorithm is suitable for implementation on multiprocessor systems and is able to concurrently mask processor failures. A fast algorithm based on long division for detecting and correcting multiple processor failures is presented. Moduli polynomials that yield an efficient and robust fast-Fourier transform (FFT)-based algorithm are selected. For this implementation, a single fault detection and correction is studied, and a generalized-likelihood-ratio test is applied to optimally detect system failures in the presence of computational noise. The coding scheme is capable of protecting over 90% of the computation involved in convolution. Parts not covered by the scheme are assumed to be protected via triple modular redundancy. This hybrid approach can detect and correct any single system failure with as little as 70% overhead, compared with 200% needed for a system fully protected via modular redundancy