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.

翻译：三模冗余（TMR）是容错系统中最常用的技术之一，其输出由多数投票器决定。然而，纳米尺度时代更易发生的复制模块设计多样性或软错误可能影响多数投票方案。此外，TMR方案的高昂开销可能限制其在能耗和面积受限的关键系统中的应用。但对于关键系统（如自动驾驶车辆和机器人）中部署的大多数固有容错应用（如图像处理和视觉），达到给定可靠性水平比追求精确结果更具优先级。因此，这些应用可从近似计算范式中受益，以实现更高能效和更小面积。本文提出一种节能的近似可靠性框架（X-Rel），旨在克服TMR系统的上述挑战，并在不牺牲期望可靠性约束和输出质量的前提下充分发挥近似计算潜力。X-Rel框架基于系统化的误差边界方法放松投票器精度，该方法利用用户定义的质量与可靠性约束。随后，利用优化后的投票器尺寸近似TMR模块，从而最小化总面积和能耗。在15纳米FinFET技术下，本文评估了将所提X-Rel技术应用于TMR结构在不同质量约束及多种可靠性边界下的有效性。与现有最先进的近似TMR投票器相比，X-Rel投票器的延迟、面积和能耗分别降低高达86%、87%和98%。