Protecting convolution-type aritmetic array calculations with generalized cyclic codes

Abstract

Fault-tolerance in dense high-speed arithmetic units that calculate convolutions between arrays of data is introduced through cyclic codes which are defined over the rings and fields commonly employed by such units. New systematic encoding and data manipulation techniques make the application of these generalized cyclic codes to error detection straightforward and efficient. The necessary overhead 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.