Exploiting Errors for Efficiency: A Survey from Circuits to Algorithms

Abstract

When a computational task tolerates a relaxation of its specification or when an algorithm tolerates the effects of noise in its execution, hardware, programming languages, and system software can trade deviations from correct behavior for lower resource usage. We present, for the first time, a synthesis of research results on computing systems that only make as many errors as their users can tolerate, from across the disciplines of computer aided design of circuits, digital system design, computer architecture, programming languages, operating systems, and information theory.Rather than over-provisioning resources at each layer to avoid errors, it can be more efficient to exploit the masking of errors occurring at one layer which can prevent them from propagating to a higher layer. We survey tradeoffs for individual layers of computing systems from the circuit level to the operating system level and illustrate the potential benefits of end-to-end approaches using two illustrative examples. To tie together the survey, we present a consistent formalization of terminology, across the layers, which does not significantly deviate from the terminology traditionally used by research communities in their layer of focus.

Integer-Value Encoding for Approximate On-Chip Communication

“…Let S opt be the set of 2 3 (3-bit input data) 4-bit valid codewords for optimal mapping and Y + j be a member of this set:…”

“…To account for noise effects, we run transient-noise simulation for 100 noiseruns and different clock frequencies. The signals are expected to traverse through the interconnect in one clock cycle 3 The results are reported for the 8 th segment of the interconnect.…”

“…As stated in the international technology roadmap for semiconductors [1], delay and power consumption of the global interconnects are becoming a bottleneck; metallic wires can be either fast or dense but not both [2]. The on-chip communication is reaching the fundamental limits of the resources required for a fully reliable operation [3]. Therefore, an improvement in on-chip communication as the real limiter of the high performance integrated circuits is essential.…”

Probabilistic Value-Deviation-Bounded Source-Dependent Bit-Level Channel Adaptation for Approximate Communication

“…For these systems the effects of errors are best quantified in terms of their integer distance, rather than using a Hamming distance. At the same time, the computations that consume this data can often tolerate errors with a wide range of integer distances with limited system-level consequences [2], [3], [4].…”

“…3. The resolution (0.39 kΩ) of the ISL23415TFUZ (100 kΩ) was too coarse to have the desired accuracy of I2C error manipulation.…”