Low Cost Concurrent Error Masking Using Approximate Logic Circuits

Abstract

With technology scaling, logical errors arising due to single-event upsets and timing errors arising due to dynamic variability effects are increasing in logic circuits. Existing techniques for online resilience to logical and timing errors are limited to detection of errors, and often result in significant performance penalty and high area/power overhead. This paper proposes approximate logic circuits as a design approach for low cost concurrent error masking. An approximate logic circuit predicts the value of the outputs of a given logic circuit for a specified portion of the input space, and can indicate uncertainty about the outputs over the rest of the input space. Using portions of the input space that are most vulnerable to errors as the specified input space, we show that approximate logic circuits can be used to provide low overhead concurrent error masking support for a given logic circuit. We describe efficient algorithms for synthesizing approximate circuits for concurrent error masking of logical and timing errors. Results indicate that concurrent error masking based on approximate logic circuits can mask 88% of targeted logical errors for 34% area overhead and 17% power overhead, 100% timing errors on all timing paths within 10% of the critical path delay for 23% area overhead and 8% power overhead, and 100% timing errors on all timing paths within 20% of the critical path delay for 42% area overhead and 26% power overhead.Index Terms-Concurrent error detection, concurrent error masking, logic synthesis, reliability.

Error Mitigation Using Approximate Logic Circuits: A Comparison of Probabilistic and Evolutionary Approaches

“…Approximations can be classified as unidirectional or bidirectional [15]. An approximation is called unidirectional if the incorrect subspace is either a subset of the on-set or a subset of the off-set of G. In the first case,Ĝ is called an underapproximation or on-set unidirectional approximation of G. Similarly, in the second caseĜ is called an over-approximation or off-set unidirectional approximation of G. In the sequel, the under-approximations and over-approximations of a function G will be denoted respectively as F and H.…”

“…However, as this approach may lead to an incorrect approximation, a SAT solver is used to ensure correctness. This approach is extended in [15] by considering predictor-indicator bidirectional approximations. This type of approximations use a predictor function, that predicts the value of the function, and an indicator function, that indicates uncertainty about the predicted value.…”

“…This type of approximations use a predictor function, that predicts the value of the function, and an indicator function, that indicates uncertainty about the predicted value. The advantage of this approach is that the predictor and indicator functions are not required to have implication relationships with the original function G. However, predictor-indicator bidirectional approximations cannot be used when the bidirectional approximate circuit is vulnerable to errors [15].…”

Partial TMR in FPGAs Using Approximate Logic Circuits

“…In general, an additional logic function can be used to explicitly mark such cases, which is referred as indicator function [12]. However, this approach requires that the indicator function is robust.…”

“…Most of these methods try to approximate the implementation of logic functions using synthesis techniques [10], [11], [12], [15], [16]. Synthesis techniques depart from a functional model of the original circuit, such as a Binary Decision Diagram (BDD) [10], and apply synthesis algorithms to simplify the logic function while relaxing the constraint of matching the original In particular, references [11] and [12] use cube elimination based on the Observability Don't Cares (ODCs), [15] uses two-level minimization and [16] uses boolean factoring. A disadvantage of synthesis-based approximation techniques is that the error mitigation reduction caused by the approximation transformations is difficult to estimate, because approximation is based on functional considerations.…”