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<p><b>Abstract</b>—Algorithm-based fault tolerance (ABFT) can provide a low-cost error protection for array processors and multiprocessor systems. Several ABFT techniques (<it>weighted check-sum</it>) have been proposed to design fault-tolerant matrix operations. In these schemes, encoding/decoding uses either multiplications or divisions so that overhead is high. In this paper, new encoding/decoding methods are proposed for designing fault-tolerant matrix operations. The unique feature of these new methods is that only additions and subtractions are used in encoding/decoding. In this paper, new algorithms are proposed to construct error detecting/correcting codes with the minimum Hamming distance 3 and 4. We will show that the overhead introduced due to the incorporation of fault tolerance is drastically reduced by using these new coding schemes.</p>
Array processors, concurrent error detection/correction, error detecting/correcting codes, fault tolerance, multiprocessor systems.

Y. S. Han, D. Tao and C. Hartmann, "New Encoding/Decoding Methods for Designing Fault-Tolerant Matrix Operations," in IEEE Transactions on Parallel & Distributed Systems, vol. 7, no. , pp. 931-938, 1996.
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