A Survey on the Best Choice for Modulus of Residue Code

Nowadays, the development of technology and the growing need for dense and complex chips have led chip industries to increase their attention on the circuit testability. Also, using the electronic chips in certain industries, such as the space industry, makes the design of fault tolerant circuits a challenging issue. Coding is one of the most suitable methods for error detection and correction. The residue code, as one of the best choices for error detection aims, is wildly used in large arithmetic circuits such as multiplier and also finds a wide range of applications in processors and digital filters. The modulus value in this technique directly effect on the area overhead parameter. A large area overhead is one of the most important disadvantages especially for testing the small circuits. The purpose of this paper is to study and investigate the best choice for residue code check base that is used for simple and small circuits such as a simple ripple carry adder. The performances are evaluated by applying stuck-at-faults and transition-faults by simulators. The efficiency is defined based on fault coverage and normalized area overhead. The results show that the modulus 3 with 95% efficiency provided the best result. Residue code with this modulus for checking a ripple carry adder, in comparison with duplex circuit, 30% improves the efficiency

Design and Analysis of Multiplexer based Approximate Adder for Low Power Applications

Low power consumption is crucial for error-acceptable multimedia devices, with picture compression approaches leveraging various digital processing architectures and algorithms. Humans can assemble useful information from partially inaccurate outputs in many multimedia applications. As a result, producing exact outputs is not required. The demand for an exact outcome is fading because new innovative systems are forgiving of faults. In the domain where error-tolerance is accepted, approximate computing is a new paradigm that relaxes the requirement for an accurate modeling while offering power, time, and delay benefits. Adders are an essential arithmetic module for regulating power and memory usage in digital systems. The recent implementation and use of approximate adders have been supported by trade-off characteristics such as delay, lower power consumption. This study examines the delay and power consumption of conventional and approximate adders. Also, a simple, fast, and power-efficient multiplexer-based approximate adder is proposed, and its performance outperforms the adders compared with existing adders. The proposed adder can be utilized in error-tolerant and various digital signal processing applications where exact results are not required. The proposed and existing adders are designed using EDA software for the performance calculations. With a delay of 81 pS, the proposed adder circuit reduces power consumption compared to the exact one. The experiment shows that the designed approximate adder can be used to implement circuits for image processing systems because it has a smaller delay and uses less energy

X-Rel: Energy-Efficient and Low-Overhead Approximate Reliability Framework for Error-Tolerant Applications Deployed in Critical Systems

Triple Modular Redundancy (TMR) is one of the most common techniques in fault-tolerant systems, in which the output is determined by a majority voter. However, the design diversity of replicated modules and/or soft errors that are more likely to happen in the nanoscale era may affect the majority voting scheme. Besides, the significant overheads of the TMR scheme may limit its usage in energy consumption and area-constrained critical systems. However, for most inherently error-resilient applications such as image processing and vision deployed in critical systems (like autonomous vehicles and robotics), achieving a given level of reliability has more priority than precise results. Therefore, these applications can benefit from the approximate computing paradigm to achieve higher energy efficiency and a lower area. This paper proposes an energy-efficient approximate reliability (X-Rel) framework to overcome the aforementioned challenges of the TMR systems and get the full potential of approximate computing without sacrificing the desired reliability constraint and output quality. The X-Rel framework relies on relaxing the precision of the voter based on a systematical error bounding method that leverages user-defined quality and reliability constraints. Afterward, the size of the achieved voter is used to approximate the TMR modules such that the overall area and energy consumption are minimized. The effectiveness of employing the proposed X-Rel technique in a TMR structure, for different quality constraints as well as with various reliability bounds are evaluated in a 15-nm FinFET technology. The results of the X-Rel voter show delay, area, and energy consumption reductions of up to 86%, 87%, and 98%, respectively, when compared to those of the state-of-the-art approximate TMR voters.Comment: This paper has been published in IEEE Transactions on Very Large Scale Integration (VLSI) System