A Design Methodology of Line Feedback Shift Registers With Quantum Cellular Automata

Mingliang Zhang,Zhenglin Han,Zhigang Gu,Xiaokuo Yang,Huanqing Cui

doi:10.1109/ojnano.2021.3129858

Mingliang Zhang, Zhenglin Han + Show 3 more

Open Access

https://doi.org/10.1109/ojnano.2021.3129858

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Abstract

The quantum-dot cellular automata (QCA) present great promising advantages for emerging nano logic circuits. However, feedback design in QCA sequential circuit is often a big problem. Especially in line feedback shift registers (LFSR), each feedback loop consists of at least a modulo-2 adder and a trigger unit, which is hard to implement using the conventional methods. Given the importance of LFSR in communication systems, a design methodology with QCA is proposed in this work. At first, a new structure is presented to be used in every single feedback LFSR since it can make the feedback loop consume only one clock cycle of delay. Subsequently, quantitative criteria are presented to judge whether any multi-feedback LFSR can be directly designed using the proposed structure. LFSR that cannot satisfy the criteria are supposed to be transformed to their equivalent forms. We verify any LFSR can be transformed to the type of single feedback, according to the theorem of searching the monic and irreducible polynomials over Galois field GF (2). The step-by-step method of transforming multi-feedback into single feedback is given on the consideration of all kinds of cases. Further, two other simple transforming methods are presented to cope with the exponential growth of clock delay in the multi-to-single transforming method. The most remarkable advantage of this series of methods is to keep from introducing undesired bits into the payload data flowing in the sequential circuits.

Highlights

Quantum-dot cellular automata (QCA) is a potential candidate for the conventional logic paradigm at nano scale
There are some problems in QCA circuit design, one main of which is the implementation of feedback of the sequential circuits
In terms of a QCA sequential circuit, that means, a valid output bit of the circuit at this moment should travel along the feedback loop back to one input of a logic gate or a flip-flop and synchronize with the coming written bit

Summary

Introduction

Quantum-dot cellular automata (QCA) is a potential candidate for the conventional logic paradigm at nano scale. Information in a cell is replicated by other cells like domino effect, leaning on the field coupling between cells This "processing-in-wire" [2] paradigm shows the potential advantages of high switching speed, high integrity density, and low power dissipation compared with transistor-based technology [3]. In terms of a QCA sequential circuit, that means, a valid output bit of the circuit at this moment should travel along the feedback loop back to one input of a logic gate or a flip-flop and synchronize with the coming written bit. A false will be resulted at the output of the circuit time It is usually hard for QCA circuit to satisfy this real-time requirement. When the delay tolerance between them is small, it will be very difficult for the feedback design to satisfy the real-time requirement

Methods

Conclusion