Introducing Galois field polynomial addition in quantum-dot cellular automata

Abstract

The quantum-dot cellular automata, which provides a novel nano-computation paradigm, has got wide acceptance owing to its ultra-high operating speed, extremely low power dissipation with a considerable reduction in feature size. The QCA architectures are emerging as a potential alternative to the conventional complementary metal oxide semiconductor technology. This work mitigates the gap between QCA and coding theory, particularly finite field addition through a redesign-able, reproducible and scalable modular based approach. Primarily, a module to perform modulo-2 addition, namely M2A module is introduced. The notion of M2A module further results in a novel algorithm that generates an approach of QCA design of Galois field (GF)-based polynomial adders. The cost functions are calculated to estimate the operation of M2A-based polynomial adders, the proposed adders are compared with the conventional counterpart, and the best one is reported. The defect- and fault-tolerant behavior of GF(28) polynomial adder is also examined as a particular instance.