Fault tolerant multiplication based on convolution

Abstract:
This paper presents a new approach to the multiplication for signed numbers in two’s complement which can achieve different levels of fault tolerance by combining hardware and time redundancy. The partial products are considered as convolutions between two discrete functions and carried out by addressing recursively a Look-up table where they have been stored. The self-checking capability is achieved by the parallel calculation of two different but equivalent convolutions. The fault tolerance for transient errors is achieved by using time redundancy in each convolution thread. A very simple circuit implements the multiplier which provides encouraging results in hardware overhead compared with other well-known proposals. This paper is devoted to expose the method, development, capabilities and implementation.