An Approach to Increasing Reliability Using Syndrome Extension

Computational errors in numerical data processing may be detected efficiently by using parity values associated with real number codes, even when inherent round off errors are allowed in addition to failure disruptions. This paper examines correcting turbo codes by straightforward application of an algorithm derived for finite-field codes, modified to operate over any field. There are syndromes associated with Turbo code words corrupted by large and small error values that relate directly to the induced errors. Hence, after determining the location of a few large errors if possible, the syndromes may be extended so as to yield these large corrupting errors along with approximations to the prevalent low-level errors. The techniques proposed in this paper can be employed in correcting erroneously processed data caused by soft errors.