System level reliability in convolution computations

The author demonstrates how generalized cyclic codes, defined over the rings and fields usually used in high-speed convolution of discrete-time sequence processing, can be incorporated directly and quite naturally within the data processing of such arithmetic systems. Design methods for one class of real cyclic codes are detailed, along with examples. Encoding and parity manipulation methods are developed which permit straightforward and efficient mechanizations. Errors are detected immediately at the conclusion of the processing pass, allowing appropriate error control actions to be initiated. Typical responses to detected errors may be to retry the calculation, reconfigure the overall system, or enter a subsystem testing mode. A complexity analysis of the protection subsystems shows that protection requires additional arithmetic complexity on the order of the number of parity positions squared