28 November 1984 Fault-Tolerant Matrix Operations On Multiple Processor Systems Using Weighted Checksums
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Abstract
Hardware for performing matrix operations at high speeds is in great demand in signal and image processing and in many real-time and scientific applications. VLSI technology has made it possible to perform fast large-scale vector and matrix computations by using multiple copies of low-cost processors. Since any functional error in a high performance system may seriously jeopardize the operation of the system and its data integrity, some level of fault-tolerance must be obtained to ensure that the results of long computations are valid. A low-cost checksum scheme had been proposed to obtain fault-tolerant matrix operations on multiple processor systems. However, this scheme can only correct errors in matrix multiplication; it can detect, but not correct errors in matrix-vector multiplication, LU-decomposition, and matrix inversion. In order to solve these problems with the checksum scheme, a very general matrix encoding scheme is proposed in this paper to achieve fault-tolerant matrix operations with multiple processor systems. Since many signal and image processing algorithms involving a "multiply-and-accumulate" type of expression can be transformed into matrix-vector multiplication operations and executed in a linear array, this scheme is extremely useful for cost-effective and fault-tolerant signal and image processing.
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Jing-Yang Jou, Jacob A. Abraham, "Fault-Tolerant Matrix Operations On Multiple Processor Systems Using Weighted Checksums", Proc. SPIE 0495, Real-Time Signal Processing VII, (28 November 1984); doi: 10.1117/12.944013; https://doi.org/10.1117/12.944013
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