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：摘要：三模冗余（TMR）是容错系统中最常用的技术之一，其输出由多数表决器决定。然而，纳米尺度下模块复制设计多样性及软错误频发可能影响多数表决机制。此外，TMR方案的高昂开销会限制其在能耗与面积受限的关键系统中的应用。但对于关键系统（如自动驾驶汽车和机器人）中部署的图像处理、视觉等天然具有容错性的应用，在达到特定可靠性要求的前提下，精确结果并非首要目标。因此，此类应用可借助近似计算范式实现更高能效与更低面积消耗。本文提出一种高能效的近似可靠性框架（X-Rel），以克服上述TMR系统的挑战，在满足既定可靠性约束与输出质量的前提下充分发挥近似计算的潜力。该框架通过系统化误差边界方法放松表决器的精度要求，此方法基于用户定义的质量与可靠性约束。随后，利用简化后的表决器规模对TMR模块进行近似化处理，以最小化整体面积与能耗。在15纳米FinFET工艺节点下，评估了X-Rel技术在不同质量约束与可靠性边界条件下应用于TMR结构的有效性。与最新近似TMR表决器相比，X-Rel表决器在延迟、面积与能耗上分别降低最高达86%、87%与98%。