Data protection in convolution computations

Modern high-speed convolvers use sophisticated arithmetic units operating over large finite integer rings or with floating point approximations to the real or complex fields. However, these units are susceptible to random internal errors termed soft fails. New systematic encoding and data manipulation techniques that make error detection with generalized cyclic codes straightforward and efficient are described. Error control is attached directly to the data, permitting protection of any form of parallel or distributed system configuration. Design methods for one class of real cyclic codes are detailed. The necessary overhead for direct parity computations have complexity proportional to the number of parity symbols squared, whereas the error-detecting capability for both random and burst errors is directly related to this parity number. When certain extension fields exist, the parity calculations become linear with the number of complex operations in the extended domain