CNFET-based approximate ternary adders for energy-efficient image processing applications

Nowadays, low power design has attracted more attentions. This purpose is achieved through some techniques such as low-power design methods, multiple valued logic and more recently by approximate computing. Carbon nanotube field-effect transistor (CNFET) is an appropriate candidate device for low-power multiple valued logic applications. In approximate computing, reducing the precision of arithmetic blocks leads to reduction in power consumption. In this paper, two approximate CNFET-based ternary full adder cells are proposed. The proposed designs considerably reduce the design complexity and the number of transistors by utilizing the unique properties of CNFETs as well as the switching logic style. The simulation results demonstrate that the proposed approximate designs improve the delay, power and energy dissipation by about 90% as compared to their exact counterparts. Also, as the adder cells are commonly used in the reduction step of multiplier circuits, the efficiency of the proposed cells is investigated in the structure of ternary multipliers through the normalized error distance and power-error tradeoff metrics. Moreover, as the approximate circuits are used in image processing applications, an inexact ternary multiplier is utilized for pixel by pixel image multiplying and the results are compared with the exact ones. According to the simulation results, the proposed inexact methods enhance the performance of arithmetic circuits while maintaining the required accuracy for such applications.     

门电路延时查找表的凸平滑算法

门电路延时参数的查找表在电路逻辑综合及静态时序分析中均有重要应用。其精度及数学上的凸特性和平滑程度对电路最终的设计结果有较大的影响。基于绝大多数门电路延时模型的实际特性,提出了一种在给定查找表的基础上进行凸平滑的算法。该算法使用了计算机辅助几何设计中的张量积B样条技术,并通过调整样条系数使平滑后得到的延时模型为凸函数。为了使新延时模型的构造快速且准确,样条系数的求解过程被描述为一个半定规划问题,因此得到的新模型具有全局最小的拟合误差。最后以标准单元库门电路通过SPICE仿真得到的查找表数据为实例,并与其他方法进行对照,验证了该方法的有效性和精度。     

Machine Learning-Based Pruning Technique for Low Power Approximate Computing

Approximate Computing is a low power achieving technique that offers an additional degree of freedom to design digital circuits. Pruning is one of the types of approximate circuit design technique which removes logic gates or wires in the circuit to reduce power consumption with minimal insertion of error. In this work, a novel machine learning (ML) -based pruning technique is introduced to design digital circuits. The machine-learning algorithm of the random forest decision tree is used to prune nodes selectively based on their input pattern. In addition, an error compensation value is added to the original output to reduce an error rate. Experimental results proved the efficiency of the proposed technique in terms of area, power and error rate. Compared to conventional pruning, proposed ML pruning achieves 32% and 26% of the area and delay reductions in 8*8 multiplier implementation. Low power image processing algorithms are essential in various applications like image compression and enhancement algorithms. For real-time evaluation, proposed ML optimized pruning is applied in discrete cosine transform (DCT). It is a basic element of image and video processing applications. Experimental results on benchmark images show that proposed pruning achieves a very good peak signal-to-noise ratio (PSNR) value with a considerable amount of energy savings compared to other methods.     

Designing new ternary reversible subtractor circuits

The reducing of the width of quantum reversible circuits makes multiple-valued reversible logic a very promising research area. Ternary logic is one of the most popular types of multiple-valued reversible logic, along with the Subtractor, which is among the major components of the ALU of a classical computer and complex hardware. In this paper the authors will be presenting an improved design of a ternary reversible half subtractor circuit. The authors shall compare the improved design with the existing designs and shall highlight the improvements made after which the authors will propose a new ternary reversible full subtractor circuit. Ternary Shift gates and ternary Muthukrishnan–Stroud gates were used to build such newly designed complex circuits and it is believed that the proposed designs can be used in ternary quantum computers. The minimization of the number of constant inputs and garbage outputs, hardware complexity, quantum cost and delay time is an important issue in reversible logic design. In this study a significant improvement as compared to the existing designs has been achieved in as such that with the reduction in the number of ternary shift and Muthukrishnan-Stroud gates used the authors have produced ternary subtractor circuits.     

EDOA: an efficient delay optimization approach for mixed-polarity Reed-Muller logic circuits under the unit delay model

Delay optimization has recently attracted significant attention. However, few studies have focused on the delay optimization of mixed-polarity Reed-Muller (MPRM) logic circuits. In this paper, we propose an efficient delay optimization approach (EDOA) for MPRM logic circuits under the unit delay model, which can derive an optimal MPRM logic circuit with minimum delay. First, the simplest MPRM expression with the fewest number of product terms is obtained using a novel Reed-Muller expression simplification approach (RMESA) considering don’t-care terms. Second, a minimum delay decomposition approach based on a Huffman tree construction algorithm is utilized on the simplestMPRM expression. Experimental results on MCNC benchmark circuits demonstrate that compared to the Berkeley SIS 1.2 and ABC, the EDOA can significantly reduce delay for most circuits. Furthermore, for a few circuits, while reducing delay, the EDOA incurs an area penalty.     

对数/指数算法的改进及其VLSI实现

提出了一种二进制数的指数/对数运算的线性近似的改进算法,并VLSI实现。该算法能较好地提高精度,相比于现有最新文献提出的算法,对数运算的相对误差减少了46.1%,指数运算的相对误差减少了32.2%。实现时,设计了前导1探测电路和减小误差的误差补偿电路。该算法VLSI实现简单,只需组合逻辑就能在一个时钟周期内得到计算结果。     

Multi-objective evolutionary design and knowledge discovery of logic circuits based on an adaptive genetic algorithm

Evolutionary design of circuits (EDC), an important branch of evolvable hardware which emphasizes circuit design, is a promising way to realize automated design of electronic circuits. In order to improve evolutionary design of logic circuits in efficiency, scalability and capability of optimization, a genetic algorithm based novel approach was developed. It employs a gate-level encoding scheme that allows flexible changes of functions and interconnections of logic cells comprised, and it adopts a multi-objective evaluation mechanism of fitness with weight-vector adaptation and circuit simulation. Besides, it features an adaptation strategy that enables crossover probability and mutation probability to vary with individuals' diversity and genetic-search process. It was validated by the experiments on arithmetic circuits especially digital multipliers, from which a few functionally correct circuits with novel structures, less gate count and higher operating speed were obtained. Some of the evolved circuits are the most efficient or largest ones (in terms of gate count or problem scale) as far as we know. Moreover, some novel and general principles have been discerned from the EDC results, which are easy to verify but difficult to dig out by human experts with existing knowledge. These results argue that the approach is promising and worthy of further research.     

A new automated design and optimization method of CMOS logic circuits based on Modified Imperialistic Competitive Algorithm

This paper proposes a novel evolutionary approach based on modified Imperialist Competitive Algorithm for combinational logic circuits designing and optimization. The Imperialist Competitive Algorithm operates on real values and is not applicable to logic circuits optimization problems. So a modified version of ICA is proposed to overcome this shortcoming. Modification of the algorithm depends on random cell replacement between Imperialist and its colonies as assimilation policy. Also a multi-objective evaluation mechanism in the form of a weighted cost function is introduced to obtain optimized circuits in case of circuit area and propagation delay. To evaluate the effectiveness of this method some general benchmark circuits are used in which the circuits with fewer logic cells (minimized space) and lower propagation delay are obtained. The simulation results of our proposed method are compared with some conventional and heuristic methods. Simulation results show that our proposed method significantly improves the performance factor which represents both circuit area and propagation delay.     

The continuous non-linear approximation of procedurally defined curves using integral B-splines

This paper outlines an algorithm for the continuous non-linear approximation of procedurally defined curves. Unlike conventional approximation methods using the discrete L_2 form metric with sampling points, this algorithm uses the continuous L_2 form metric based on minimizing the integral of the least square error metric between the original and approximate curves. Expressions for the optimality criteria are derived based on exact B-spline integration. Although numerical integration may be necessary for some complicated curves, the use of numerical integration is minimized by a priori explicit evaluations. Plane or space curves with high curvatures and/or discontinuities can also be handled by means of an adaptive knot placement strategy. It has been found that the proposed scheme is more efficient and accurate compared to currently existing interpolation and approximation methods.     

Low power noise immune node voltage comparison keeper design for high speed architectures

The demand for high speed and area minimization has directed the designers towards dynamic CMOS logic design. The domino logic is one of the famous logic in dynamic CMOS logic. The designer needs to compromise the circuit speed and power consumption to reduce the impact of noise in domino logic circuit design. In this work, low power domino logic circuit is proposed to decrease power consumption with improvement in noise immunity. The low power consumption is achieved at the cost small sacrifice in delay. However, the proposed logic circuit has attained better Power Delay Product (PDP) as compared to existing noise tolerant circuits. The experimental simulation results shows the proposed logic exhibit 3.4% power reduction when compared with the low power domino logic circuit [10] for two input OR gates. The proposed logic had a little compromise with delay in the existing logics. However, the Power Delay Product (PDP) of proposed logic circuit has reduced as compared to existing techniques. The proposed logic also provides the better improvement in noise immunity parameters such as UNG and ANTE as compared to the existing logics. The proposed logic circuit based application circuit such as 4:1 multiplexer also provides better improvement in case of power consumption and noise immunity.     

Novel designs of nanometric parity preserving reversible compressor

Reversible logic is a new field of study that has applications in optical information processing, low power CMOS design, DNA computing, bioinformatics, and nanotechnology. Low power consumption is a basic issue in VLSI circuits today. To prevent the distribution of errors in the quantum circuit, the reversible logic gates must be converted into fault-tolerant quantum operations. Parity preserving is used to realize fault tolerant in this circuits. This paper proposes a new parity preserving reversible gate. We named it NPPG gate. The most significant aspect of the NPPG gate is that it can be used to produce parity preserving reversible full adder circuit. The proposed parity preserving reversible full adder using NPPG gate is more efficient than the existing designs in term of quantum cost and it is optimized in terms of number of constant inputs and garbage outputs. Compressors are of importance in VLSI and digital signal processing applications. Effective VLSI compressors reduce the impact of carry propagation of arithmetic operations. They are built from the full adder blocks. We also proposed three new approaches of parity preservation reversible 4:2 compressor circuits. The third design is better than the previous two in terms of evaluation parameters. The important contributions have been made in the literature toward the design of reversible 4:2 compressor circuits; however, there are not efforts toward the design of parity preservation reversible 4:2 compressor circuits. All the scales are in the nanometric criteria.     

Speeding up processing with approximation circuits

Current microprocessors employ a global timing reference to synchronize data transfer. A synchronous system must know the maximum time needed to compute a function, but a circuit usually finishes computation earlier than the worst-case delay. The system nevertheless waits for the maximum time bound to guarantee a correct result. As a first step in achieving variable pipeline delays based on data values, approximation circuits can increase clock frequency by reducing the number of cycles a function requires. Instead of implementing the complete logic function, a simplified circuit mimics it using rough calculations to predict results. The results are correct most of the time, and simulations show improvements in overall performance in spite of the overhead needed to recover from mistakes.     

Modeling Combinational Circuits Using Linear Word-level Structures

In many applications of circuit design and synthesis, it is natural and in some instances essential to manipulate logic functions and model circuits using word-level representations and arithmetic operations in contrast to bit-level representations and logic operations. This paper reviews linear word-level structures and formulates their properties for combinational circuit modeling. The paper addresses the following problem: given a library of gates with their corresponding word-level representations such as linear arithmetic expressions or respective graph structures, find a word-level model of an arbitrary combinational circuit/netlist using that library of gates and minimizing memory allocation and time delay requirements. We present a comprehensive study on linearization assuming various circuit processing strategies. In particular, we develop a new approach to manipulate linear word-level representations by means of cascades. The practical applicability of linear structures and developed algorithms is strengthen by considering the problem of timing analysis. All this is supported by the experimental study on benchmark circuits.     

Delay and area efficient approximate multiplier using reverse carry propagate full adder

The performance and power of error resilient applications will rise with a decrease in designing complexness due to approximate computing. This paper includes the new method for the approximation of multipliers. Variable likelihood terms are produced by the alteration of partial products of the multiplier. Based on the probability statistics, the accumulation of altered partial products leads to the variation of logic complexity. Here the estimate is implemented in 2 variables of 16-bit multiplier and in the final stage with reverse carry propagate adder(RCPA). The reverse carry propagate adder have carry signal propagation from the most significant bit(MSB) to the least significant bit(LSB), which results in greater relevance to the input carry than the output carry. The technique of carry circulation in reverse order with delay variations increases the stability. Utilizing the RCPA in approximate multiplier provide 21% and 7% improvements in area and delay. On comparing, this structure is resilient to delay variations than the ideal approximate adder.     

Area-Delay-Energy aware SRAM memory cell and M × N parallel read/write memory array design for quantum dot cellular automata

Quantum dot Cellular Automata (QCA) is an emerging nanotechnology, potentially suitable to replace the popular technologies like Complementary Metal Oxide Semiconductor (CMOS) technology. The evolution of QCA has become prominent due to high operating frequency, nanoscale device and zero current low power nanotechnology. However, the Area-Delay-Energy aware QCA logic circuit design remains a prime concern in this post CMOS technology. In this work the primary attention is given to build efficient QCA circuits. The motivation of this work is to propose Efficient VLSI design in terms of Area, Delay, Power and PDP (Power delay product). Different methodologies are reported to design a combinational and sequential circuit in QCA technology. An extensive focus is given in designing of 3 different QCA based Area-Delay-Energy aware SRAM memory cells, parallel read/write M × N SRAM memory array and peripherals like decoder and multiplexer. Since appropriate signal distribution network (SDN) is an essential aspect to deign QCA circuit, it has also been reported a delay aware signal distribution methodology applicable for any type of QCA logic circuit design. The significant results of this research finding are expressed in terms of Area-Delay-Energy dissipation tradeoff. When compared with respective to the state of art, the performance metric of proposed QCA based memory cells are excelled, on an average 40% reduction in area, 33% and 22% drop in delay and energy dissipation respectively are achieved for proposed three different memory cell design.     

Design of low power multi-ternary digit multiplier in CNTFET technology

This work introduces the method to implement energy efficient designs of arithmetic units such as a ternary full adder, ripple carry adder, single-trit multiplier and multi-trit multiplier using carbon nanotube field effect transistors (CNTFETs). A CNTFET unique feature of the threshold voltage variation by changing the CNT diameter, make it a suitable alternative for being employed in ternary logic designs. In designing the proposed circuits, decoder circuit functionality is realized by various threshold detector circuits tuned to a specific logical threshold voltage value. The multiplier circuit is designed by combing the capacitive logic and the minority function. In order to test the practicability of proposed circuits in cascaded circuits, multi-digit adder and multiplier circuits are constructed. The proposed multi-digit multiplier structure is based on classical Wallace multiplier and includes various optimized versions of adder and multiplier circuits. Extensive simulation has been done to examine the competency of proposed designs under different test conditions. The design of 3-trit multiplier formed by combing the proposed adder and multiplier circuits shows 16 times reduction in power consumption as well as energy consumption in comparison to previous multiplier design.     

Design of reversible logic based full adder in current-mode logic circuits

Demand of Very Large Scale Integration (VLSI) circuits with very high speed and low power are increased due to communication system's transmission speed increase. During computation, heat is dissipated by a traditional binary logic or logic gates. There will be one or more input and only one output in irreversible gates. Input cannot be reconstructed using those outputs. In low power VLSI, reversible logic is commonly preferred in recent days. Information is not lost in reversible gates and back computation is possible in reversible circuits with reduced power dissipation. Reversible full adder circuits are implemented in the previous work to optimize the design and speed of the circuits. Reversible logic gates like TSG, Peres, Feynman, Toffoli, Fredkin are mostly used for designing reversible circuits. However it does not produced a satisfactory result in terms of static power dissipation. In this proposed research work, reversible logic is implemented in the full adder of MOS Current-Mode Logic (MCML) to achieve high speed circuit design with reduced power consumption. In VLSI circuits, reliable performance and high speed operation is exhibited by a MCML when compared with CMOS logic family. Area and better power consumption can be produced implementing reversible logic in full adder of MCML. Minimum garbage output and constant inputs are used in reversible full adder. The experimental results shows that the proposed designed circuit achieves better performance compared with the existing reversible logic circuits such as Feynman gate based FA, Peres gate based FA, TSG based FA in terms of average power, static power dissipation, static current and area.     

组合逻辑电路的软错误率自动分析平台

为在设计阶段快速评估集成电路的软错误率,以指导高可靠集成电路的设计,提出一种适用于组合逻辑电路和时序逻辑电路组合逻辑部分的快速软错误率自动分析平台HSECT-ANLY.采用精确的屏蔽概率计算模型来分析软错误脉冲在电路中的传播;用向量传播和状态概率传播的方法来克服重汇聚路径的影响,以提高分析速度;使用LL(k)语法分析技术自动解析Verilog网表,使分析过程自动化,且使得本平台可分析时序电路的组合逻辑部分.开发工作针对综合后Verilog网表和通用的标准单元库完成,使得HSECT-ANLY的实用性更强.对ISCAS'85和ISCAS'89 Benchmark电路进行分析实验的结果表明:文中方法取得了与同类文献相似的结果,且速度更快,适用电路类型更多,可自动分析电路的软错误率并指导高可靠集成电路的设计.     

基于互补电阻开关的忆阻乘法器设计

现有的忆阻算术逻辑多采用单个忆阻器作为存储单元,在忆阻交叉阵列中易受到漏电流以及设计逻辑电路时逻辑综合复杂度高的影响,导致当前乘法器设计中串行化加法操作的延时和面积开销增加。互补电阻开关具有可重构逻辑电路的运算速度和抑制忆阻交叉阵列中漏电流的性能,是实现忆阻算术逻辑的关键器件。提出一种弱进位依赖的忆阻乘法器。为提升忆阻器的逻辑性能,基于互补电阻开关电路结构,设计两种加法器的优化方案,简化操作步骤。在此基础上,通过改进传统的乘法实现方式,并对进位数据进行拆解,降低运算过程中进位数据之间的依赖性,实现并行化的加法运算。将设计的乘法器映射到混合CMOS/crossbar结构中,乘法计算性能得到大幅提高。在Spice仿真环境下验证所提乘法器的可行性。仿真实验结果表明,与现有的乘法器相比,所提乘法器的延时开销从O(n²)降低为线性级别,同时面积开销降低约70%。     

An Optimized Deep-Learning-Based Low Power Approximate Multiplier Design

Approximate computing is a popular field for low power consumption that is used in several applications like image processing, video processing, multimedia and data mining. This Approximate computing is majorly performed with an arithmetic circuit particular with a multiplier. The multiplier is the most essential element used for approximate computing where the power consumption is majorly based on its performance. There are several researchers are worked on the approximate multiplier for power reduction for a few decades, but the design of low power approximate multiplier is not so easy. This seems a bigger challenge for digital industries to design an approximate multiplier with low power and minimum error rate with higher accuracy. To overcome these issues, the digital circuits are applied to the Deep Learning (DL) approaches for higher accuracy. In recent times, DL is the method that is used for higher learning and prediction accuracy in several fields. Therefore, the Long Short-Term Memory (LSTM) is a popular time series DL method is used in this work for approximate computing. To provide an optimal solution, the LSTM is combined with a meta-heuristics Jellyfish search optimisation technique to design an input aware deep learning-based approximate multiplier (DLAM). In this work, the jelly optimised LSTM model is used to enhance the error metrics performance of the Approximate multiplier. The optimal hyperparameters of the LSTM model are identified by jelly search optimisation. This fine-tuning is used to obtain an optimal solution to perform an LSTM with higher accuracy. The proposed pre-trained LSTM model is used to generate approximate design libraries for the different truncation levels as a function of area, delay, power and error metrics. The experimental results on an 8-bit multiplier with an image processing application shows that the proposed approximate computing multiplier achieved a superior area and power reduction with very good results on error rates.