Some ideas about fault-tolerant Chinese Remaindering

Abstract

We present some algorithms for performing Chinese Remaindering allowing for the fact that one or more residues may be erroneous — we suppose also that an a priori upper bound on the number of erroneous residues is known. A specific application would be for residue number codes (as distinct from quadratic residue codes). We generalise the method of Ramachandran, and present two general algorithms for this problem, along with two special cases one of which uses the minimal number Chinese Remainderings (for two errors), and the other uses 12 compared with the lower bound of 10 Chinese Remainderings. These algorithms are best suited to the case where errors are unlikely; we compare with a method based on continued fractions. Our methods use only the standard Chinese remaindering operation and equality testing of the reconstructed values.