Reliability levels for fault-tolerant linear processing using real number error correction

Fault-tolerant linear processing systems using real number codes, as in algorithm-based fault tolerance methodologies, can be extended to include error correction for correcting intermittent errors in the processed output data. The reliability function for a protected system containing correction is considered under simple but realistic assumptions on the arrival of failures in both the normal processing and corrector subassemblies. An error-correcting procedure employing a real, convolutional code is described briefly, and a system diagram of a corrector subsystem containing self-checking comparators for detecting its internal failures is presented. Failures are modelled as arriving according to Poisson processes in both parts of the fault-tolerant system. Formulas for the reliability of the protected system are given and an efficient lower bound is developed. This bound depends only on broad details such as relative areas used in a VLSI design of the processing and corrector parts. Computational methods employing computer algebra packages are discussed, and some typical reliability curves for two configurations demonstrate the dramatic improvement which error correction introduces