Nonconcurrent Error Correction in the Presence of Roundoff Noise

This paper analyzes the effects of roundoff noise on our ability to nonconcurrently detect and identify transient faults that corrupt state variables during the operation of a fault-tolerant discrete-time (DT) linear time-invariant (LTI) dynamic system. Our analysis provides insight that leads to a decoding algorithm which is based on the Peterson-Gorenstein-Zierler (PGZ) algorithm and which allows us to handle roundoff noise via explicit bounds on the precision needed to guarantee the correct identification of the number of errors. The performance of our algorithm in the presence of roundoff noise is evaluated via both analytic means and simulations. As suggested by our simulations, our analytical bounds can be very tight for certain choices of design parameters and can be used to provide guidance about the design of the fault-tolerant system. These results have immediate implications for digital implementations of LTI dynamic systems (e.g. fault-tolerant digital filters) because these implementations unavoidably have to deal with finite precision effects