A Theoretical Foundation For The Weighted Checksum Scheme
Cynthia J. Anfinson, Richard P. Brent, Franklin T. Luk · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
The weighted checksum scheme has been proposed as a low-cost error detection procedure for parallel matrix computations. Error correction has proved to be a much more difficult problem to solve than detection when using weighted checksums. In this paper we provide a theoretical basis for the correction problem. We show that for a distance d+1 weighted checksum scheme, if a maximum of ici [d/2] errors ensue then we can determine exactly how many errors have occurred. We further show that in this case we can correct the errors and give a procedure for doing so.