Fault-tolerant digital filtering architectures using fast finite field transforms

Abstract

Digital filtering architectures for highly parallel realizations containing distributed error control are presented. They involve the interconnection of fault-tolerant sections using finite field arithmetic into which powerful cyclic error-correcting codes can be imbedded naturally. Realizations employing finite field transform domains and new techniques for protecting the transform coefficients are developed. These coefficients' special property, called the Chord Property, permits error detection and correction in the transform domain, and the proper selection of certain code parameters can expand this capability. Fast Transform algorithms with distributed error-control are possible because the interstage variables also obey limited chord properties. The interplay between these properties and certain code parameters are used to eliminate undesirable error propogation and provide reliable digital filter realizations.