Issue No. 04 - April (1990 vol. 39)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.54836
<p>A generalization of existing real numer codes is proposed. It is proven that linearity is a necessary and sufficient condition for codes used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU decomposition. It is also proven that for every linear code defined over a finite field, there exists a corresponding linear real-number code with similar error detecting capabilities. Encoding schemes are given for some of the example codes which fall under the general set of real-number codes. With the help of experiments, a rule is derived for the selection of a particular code for a given application. The performance overhead of fault tolerance schemes using the generalized encoding schemes is shown to be very low, and this is substantiated through simulation experiments.</p>
real number codes; encoding; fault-tolerant matrix operations; processor arrays; linearity; necessary and sufficient condition; multiplication; transposition; LU decomposition; error detecting; performance overhead; simulation experiments; encoding; error detection codes; fault tolerant computing.
V.S.S. Nair, J.A. Abraham, "Real-Number Codes for Fault-Tolerant Matrix Operations on Processor Arrays", IEEE Transactions on Computers, vol. 39, no. , pp. 426-435, April 1990, doi:10.1109/12.54836