Detecting Multiple Faults in One-Dimensional Arrays of Reversible QCA Gates

Reversible logic design is a well-known paradigm in digital computation. In this paper, quantum-dot cellular automata (QCA) is investigated for testable implementations of reversible logic in array systems. Testability of 1D arrays consisting of reversible QCA gates is investigated for multiple faulty modules. It has been shown that fault masking is possible in the presence of multiple faults without additional lines for controllability and observability. A technique for achieving C-testability of a 1D array is introduced by adding lines for observability. By adding lines for controllability, as well as observability, the array may be fully tested with a smaller number of test patterns. Different cases of arrays made of QCA reversible gates are presented to illustrate the applicability of the proposed testing method.

Modular Design of testable reversible ALU by QCA multiplexer with increase in programmability

The quantum-dot cellular automata have emerged as one of the potential computational fabrics for the emerging nanocomputing systems due to their ultra-high speed and integration density. On the other hand, reversible computing promises low power consuming circuits by nullifying the energy dissipation during the computation. This work targets the design of a reversible arithmetic logic unit (RALU) in the quantum-dot cellular automata (QCA) framework. The design is based on the reversible multiplexer (RM) synthesized by compact 2:1 QCA multiplexers introduced in this paper. The proposed reversible multiplexer is able to achieve 100% fault tolerance in the presence of single missing or additional cell defects in QCA layout. Furthermore, the advantage of modular design of reversible multiplexer is shown by its application in synthesizing the RALU with separate reversible arithmetic unit (RAU) and reversible logic unit (RLU). The RALU circuit can be tested for classical unidirectional stuck-at faults using the constant variable used in this design. The experimentation establishes that the proposed RALU outperforms the conventional reversible ALU in terms of programming flexibility and testability.     

Computational analysis and comparison of reversible gates for design and test of logic circuits

Quantum computing is one of the most significant anticipation towards the accomplishment of interminable consumer demands of small, high speed, and low-power operable electronics devices. As reversible logic circuits have direct applicability to quantum circuits, design and synthesis of these circuits are finding grounds for emerging nano-technologies of quantum computing. Multiple Controlled Toffoli (MCT) and Multiple Controlled Fredkin (MCF) are the fundamental reversible gates that playing key role in this phase of development. A number of special reversible gates have also been presented so far, which were claimed superior for providing certain purposes like logic development and testing. This paper critically analyses a range of these gates to procure an optimal solution for design, synthesis and testing of reversible circuits. The experimentation is facilitated at three subsequent levels, i.e. gates properties, quantum cost and design & testability. MCT and MCF gates are found up to 50% more cost-effective than special gates at design level and 34.4% at testability level. Maximum reversibility depth (MRD) is included as a new measurement parameter for comparison. Special gates exhibit MRD up to 7 which ideally should be 1 for a system to be physically reversible as that of MCT and MCF gates.     

Highly testable design of BiCMOS logic circuits

Most of the work reported in the literature to date on the testability of BiCMOS circuits has concentrated on fault characterization and the need for a suitable testing method that can address the peculiarities of BiCMOS circuits. The problem of adequately testing large BiCMOS logic networks remains open and complex. In this paper, we introduce a new design for testability technique for BiCMOS logic gates that results in highly testable BiCMOS logic circuits. The proposed design incorporates two features: a test charge/discharge path and built-in current sensing (BICS). The test charge/discharge path is activated only during testing and facilitates the testing of stuck-open faults using single test vectors. BICS facilitates testing of faults that cause excessive IDDQ. HSPICE simulation results show that the proposed design can detect stuck-open faults at a test speed of 10 MHz. Faults causing excessive IDDQ are detected by BICS with a detection time of 1 ns and a settling time of 2 ns. Impact of the proposed design on normal operation is minimal. The increase in propagation delay in normal operation is less than 3%. This compares very favorably with CMOS BICS reported in the literature, where the propagation delay increase was 20%, 14.4% respectively. The increase in the area is less than 15%     

Testability analysis and fault modeling of BiCMOS circuits

Defect models have been used for testability analysis of BiCMOS circuits and the results have been compared with an analysis of CMOS circuits. Using a nominal point approach, faults generated are classified as logical or performance degradation faults. It is found that logical fault testing can only cover a small percentage of the total fault set, 54% for BiCMOS, versus 69% for equivalent CMOS gates. Delay faults and current faults are analyzed as applied to BiCMOS and CMOS gates. It is shown that logical fault testing in conjunction with either delay fault testing or current fault testing promises the highest fault coverage for BiCMOS logic gates, around 95%.This research was partially supported by the Department of National Defence of Canada, Academic Research Program, grant # 3705-921.     

An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits

Reversible logic has gained interest of researchers worldwide for its ultra-low power and high speed computing abilities in the future quantum information processing. Testing of these circuits is important for ensuring high reliability of their operation. In this work, we propose an ATPG algorithm for reversible circuits using an exact approach to generate CTS (Complete Test Set) which can detect single stuck-at faults, multiple stuck-at faults, repeated gate fault, partial and complete missing gate faults which are very useful logical fault models for reversible logic to model any physical defect. Proposed algorithm can be used to test a reversible circuit designed with k-CNOT, Peres and Fredkin gates. Through extensive experiments, we have validated our proposed algorithm for several benchmark circuits and other circuits with family of reversible gates. This algorithm produces a minimal and complete test set while reducing test generation time as compared to existing state-of-the-art algorithms. A testing tool is developed satisfying the purpose of generating all possible CTS’s indicating the simulation time, number of levels and gates in the circuit. This paper also contributes to the detection and removal of redundant faults for optimal test set generation.     

Design metal-dot based QCA circuits using SPICE model

This paper proposes a SPICE model development methodology for quantum-dot cellular automata (QCA) cells and presents a SPICE model for QCA cells. The model is validated by simulating the basic logic gates such as inverter and majority voter. The proposed model makes it possible to design and simulate QCA combinational circuits and hybrid circuits of QCA and other NANO devices using SPICE. In the second half part of the paper, SET and QCA co-design methodology is proposed and SET is used as a readout interface of the QCA cell array. The SET and QCA hybrid circuit is a promising nano-scale solution.     

Automatic Test Generation for Combinational Threshold Logic Networks

We propose an automatic test pattern generation (ATPG) framework for combinational threshold networks. The motivation behind this work lies in the fact that many emerging nanotechnologies, such as resonant tunneling diodes (RTDs), single electron transistor (SET), and quantum cellular automata (QCA), implement threshold logic. Consequently, there is a need to develop an ATPG methodology for this type of logic. We have built the first automatic test pattern generator and fault simulator for threshold logic which has been integrated on top of an existing computer-aided design (CAD) tool. These exploit new fault collapsing techniques we have developed for threshold networks. We perform fault modeling, backed by HSPICE simulations, to show that many cuts and shorts in RTD-based threshold gates are equivalent to stuck-at faults at the inputs and output of the gate. Experimental results with the MCNC benchmarks indicate that test vectors were found for all testable stuck-at faults in their threshold network implementations.     

The OR-k method for on-line checking of programmable logic arrays

A programmable logic array (PLA) is nonconcurrent if every input pattern selects exactly one product term. We relax this requirement to limited concurrency where all product terms selected by the same input pattern must have identical output parts. A new testing method, OR-k testability, is developed for the on-line (concurrent) checking of limited concurrency PLAs. OR-k testing detects errors due to the selection of one or more extra product terms, and a conventional two-rail parity check on the outputs detects the other errors from single stuck-at, bridging, cross-point and broken line faults. The output patterns of an OR-k testable PLA must be unordered. For such PLAs, certain subsets of the outputs take on an all 1's pattern only in the presence of an extra product term error condition. A limited concurrency PLA tested by OR-k testability is strongly fault secure.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.     

A Test Generation Framework for Quantum Cellular Automata Circuits

In this paper, we present a test generation framework for quantum cellular automata (QCA) circuits. QCA is a nanotechnology that has attracted recent significant attention and shows promise as a viable future technology. This work is motivated by the fact that the stuck-at fault test set of a circuit is not guaranteed to detect all defects that can occur in its QCA implementation. We show how to generate additional test vectors to supplement the stuck-at fault test set to guarantee that all simulated defects in the QCA gates get detected. Since nanotechnologies will be dominated by interconnects, we also target bridging faults on QCA interconnects. The efficacy of our framework is established through its application to QCA implementations of MCNC and ISCAS'85 benchmarks that use majority gates as primitives     

Efficient design of parity preserving logic in quantum-dot cellular automata targeting enhanced scalability in testing

Design of parity preserving logic based on emerging nanotechnology is very limited due to present technological limitation in tackling its high error rate. In this work, Quantum-dot cellular automata (QCA), a potential alternative to CMOS, is investigated for designing easily testable logic circuit. A novel self-testable logic structure referred to as the testable-QCA (t-QCA), using parity preserving logic, is proposed. Design flexibility of t-QCA then evaluated through synthesis of standard functions. The programmability feature of t-QCA is utilized to implement an ALU, realizing six important functions. Although the parity preservation property of t-QCA enables concurrent detection of permanent as well as the transient faults, an augmented test logic circuit (TC) using QCA primitives has been introduced to cover the cell defects in nanotechnology. Experimental results establish the efficiency of the proposed design that outperforms the existing technologies in terms of design cost and test overhead. The achievement of 100% stuck-at fault coverage and the 100% fault coverage for single missing/additional cell defects in QCA layout of the t-QCA gate, address the reliability issues of QCA nano-circuit design.     

基于量子元胞自动机的PLA故障分析和检测

量子元胞自动机(quantum-dot cellular automata,QCA)可编程逻辑阵列(programma-ble logic array,PLA)结构可用于实现大规模可编程逻辑电路。分析了4种故障类型发生在PLA单元的8个区域中的影响,得出了具体的影响效果。其中,直接或间接致使隐含线和与门发生逻辑错误的故障均会导致PLA中故障所在行整行失效,其他故障只会影响故障所在的PLA单元的逻辑功能和配置,而对PLA中的其他单元没有影响。此外,基于故障分析,提出了具体的PLA故障检测方法。     

Design of reliable universal QCA logic in the presence of cell deposition defect

The emergence of Quantum-dot Cellular Automata (QCA) has resulted in being identified as a promising alternative to the currently prevailing techniques of very large scale integration. QCA can provide low-power nanocircuit with high device density. Keeping aside the profound acceptance of QCA, the challenge that it is facing can be quoted as susceptibility to high error rate. The work produced in this article aims towards the design of a reliable universal logic gate (r-ULG) in QCA (r-ULG along with the single clock zone and r-ULG-II along with multiple clock zones). The design would include hybrid orientation of cells that would realise majority and minority, functions and high fault tolerance simultaneously. The characterisation of the defective behaviour of r-ULGs under different kinds of cell deposition defects is investigated. The outcomes of the investigation provide an indication that the proposed r-ULG provides a fault tolerance of 75% under single clock zone and a fault tolerance of 100% under dual clock zones. The high functional aspects of r-ULGs in the implementation of different logic functions successfully under cell deposition defects are affirmed by the experimental results. The high-level logic around the multiplexer is synthesised, which helps to extend the design capability to the higher-level circuit synthesis.     

Design for concurrent error detection and testability instorage/logic arrays

Storage/Logic Arrays (SLA's) represent a structured logic array approach to the design of VLSI sequential logic. Design for concurrent error detection and testability is complicated in these arrays by the presence of embedded memory elements and multiple levels of logic. A means of designing SLA's for ease of testability and concurrent error detection (CED) is provided in this paper. Test sets for static and dynamic CMOS circuits are described. Fault and error coverage is presented and performance and area costs are analyzed for example circuits. In addition, a means of implementing dynamic CMOS SLA's is presented and shown superior to previous NMOS, static CMOS, and dynamic CMOS approaches based upon power consumption and simplicity of design     

Debugging reversible circuits

A strong driving force for research of post-CMOS technologies is the fact that silicon-based transistors cannot be arbitrarily scaled down. Furthermore, power dissipation is a major barrier in the development of smaller and more efficient computer chips. In contrast, reversible logic with its applications e.g. in low-power design or quantum computation provides a promising alternative to traditional technologies. While there have been investigations in the domain of reversible logic synthesis, testing, and verification; debugging of reversible circuits has not yet been considered. The goal of debugging is to determine gates of an erroneous circuit that explain the observed incorrect behavior.In this paper, we propose the first approach for automatic debugging of reversible Toffoli circuits. Our method uses a formulation for the debugging problem based on Boolean satisfiability. We show the differences to traditional (irreversible) debugging. In addition, we introduce an improved approach that strengthens error candidate identification. This overcomes the limitations from traditional debugging, i.e. that error candidates are only an approximation of the real source of the error. Furthermore, observations are presented that can be applied to automatically fix an erroneous circuit just by replacing a single gate by a cascade. Due to reversibility this cascade can be efficiently computed. Experimental results show the quality and efficiency of our debugging approaches.     

Design of testable reversible latches by using a novel efficient implementation of Fredkin gate

ABSTRACT

Energy dissipation caused by information loss in irreversible computations will be an important limitation for the development of nano-scale circuits in the near future. Reductions in energy dissipation comprise one of the important goals of nanotechnology-based methods, including Quantum dot Cellular Automata (QCA), and so it is desirable to consider reversibility in the design of QCA circuits. In this research, a novel reversible Fredkin gate based on QCA is proposed, which is more efficient and less complex than the conventional Fredkin gate. Conservative reversible logic is parity preserving; hence, any permanent or transient fault can be caused a mismatch between the inputs and the outputs and can be concurrently detected if a reversible circuit is implemented with the conservative Fredkin gate. A single missing/additional cell defect is investigated in the proposed Fredkin gate and fault patterns are presented. To demonstrate the efficiency of the proposed design, some testable reversible sequential elements, such as D-latch, JK-latch, T-latch and SR-latch, are designed by using it. Our proposed concurrent testable designs greatly reduce the occupied area and maximise the circuit density in comparison with previously reported designs. The proposed designs are simulated and verified using QCA Designer ver.2.0.3 and HDLQ.     

Fault characterization, testing considerations, and design fortestability of BiCMOS logic circuits

The results of a simulation-based fault characterization study of BiCMOS logic circuits are given. Based on the fault characterization results, the authors have studied different techniques for testing BiCMOS logic circuits. The effectiveness of stuck-at fault testing, stuck-open fault testing, delay fault testing, and current testing in achieving a high level of defect coverage is studied. A novel BiCMOS circuit structure that improves the testability of BiCMOS digital circuits is presented     

Adder design using 5-input majority gate in a novel “Multilayer Gate Design Paradigm” for Quantum Dot Cellular Automata Circuits

This paper proposes a novel design paradigm for circuits designed in quantum dot cellular automata (QCA) technology. Previously reported QCA circuits in the literature have generally been designed in a single layer which is the main logical block in which the inverter and majority gate are on the base layer, except for the parts where multilayer wire crossing was used. In this paper the concept of multilayer wire crossing has been extended to design logic gates in multilayers. Using a 5-input majority gate in a multilayer, a 1-bit and 2-bit adder have been designed in the proposed multilayer gate design paradigm. A comparison has been made with some adders reported previously in the literature and it has been shown that circuits designed in the proposed design paradigm are much more efficient in terms of area, the requirement of QCA cells in the design and the input-output delay of the circuit. Over all, the availability of one additional spatial dimension makes the design process much more flexible and there is scope for the customizability of logic gate designs to make the circuit compact.     

Novel designs for fault tolerant reversible binary coded decimal adders

Reversible logic circuits have received emerging attentions in recent years. Reversible logic is widely applied in some new technical fields, such as quantum computing, nanocomputing and optical computing and so on. In this paper, three fault tolerant gates are proposed, ZPL gate, ZQC gate and ZC gate. By using the proposed gates, fault tolerant quantum and reversible BCD adder and skip carry BCD adder are designed, which overcome the limitations of the existing methods. The proposed reversible BCD adders have also parity-preserving property. They are better than the existing counterparts, especially in the quantum cost. Proposed designs have been compared with existing designs with respect to the number of gates, number of garbage outputs and quantum cost.     

基于量子细胞自动机的数值比较器设计

量子细胞自动机(QCA)可以构建逻辑门和QCA线。该文基于QCA设计了1位,4位和8位数值比较器,并用QCADesigner软件进行模拟。结果表明,所设计的电路具有正确的逻辑功能。通过对电路所需细胞数、面积和时延三方面性能分析,表明所设计的电路时延并不随输入位数呈线性增加,因而所设计的电路具有良好的时延性。