Fault-Tolerant Convolution Via Chinese Remainder Codes Constructed From Non-Coprime Moduli

This paper develops a framework for performing fault-tolerant convolution via error-correcting codes based on the chinese remainder theorem (CRT) with non-coprime moduli. In contrast to convolution that is protected through CRT codes with coprime moduli, our scheme allows errors to be detected and located in a highly parallel manner, and has the advantage of being robust to faults that occur during the error handling stage. In addition, for certain important classes of errors, the codes developed in this paper require less redundancy than CRT codes constructed from coprime moduli. We demonstrate the applicability and advantages of our codes by comparing them to both CRT codes with coprime moduli and repetition codes. We focus on codes over polynomial rings, but our constructions apply naturally to integer codes; we discuss this extension and show that it generalizes the distance properties and error correction strategies associated with previously developed approaches for codes based on non-coprime integer moduli.