Applied Nanoscience

, Volume 9, Issue 8, pp 2127–2146 | Cite as

Introducing Galois field polynomial addition in quantum-dot cellular automata

  • Chiradeep MukherjeeEmail author
  • Saradindu Panda
  • Asish Kumar Mukhopadhyay
  • Bansibadan Maji
Original Article


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.


Layered T gate QCA Design rules of QCA Galois field-based polynomial addition Cost function Defect- and fault-tolerant QCA layout 



The authors are thankful to Prof. Debdatta Banerjee for her insightful comments in the field.


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Copyright information

© King Abdulaziz City for Science and Technology 2019

Authors and Affiliations

  1. 1.Department of Electronics and Communication EngineeringUniversity of Engineering and ManagementJaipurIndia
  2. 2.Department of Electronics and Communication EngineeringNational Institute of TechnologyDurgapurIndia
  3. 3.Department of Electronics and Communication EngineeringNarula Institute of TechnologyKolkataIndia

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