  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.
