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

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.