Leveraging Error Resilience of Iterative Algorithms for Energy Efficiency: from Concept to Implementation

TL;DR

This work tackles energy efficiency for iterative algorithms by exploiting their intrinsic tolerance to approximation. It introduces Adaptive-SAM, a high-level error-resilience analysis that quantifies how many initial iterations can be executed approximately, and a heterogeneous two-core LS accelerator that processes early iterations approximately and later iterations exactly. Through a radio astronomy calibration case (StEFCal), the authors demonstrate about 23% energy savings with preserved convergence and acceptable accuracy on a 40 nm LP process, supported by a detailed energy model and ASIC-level measurements. The study also argues that the traditional convergence criterion is insufficient for resilience analysis and proposes a Diff_rel metric to ensure acceptable solutions, offering a generally applicable approach to energy-efficient design of iterative workloads beyond astronomy calibration.

Abstract

Iterative algorithms are widely used in digital signal processing applications. With the case study of radio astronomy calibration processing, this work contributes towards revealing and exploiting the intrinsic error resilience of iterative algorithms for energy efficiency benefits. We consider iterative methods that use a convergence criterion as a quality metric to terminate the iterative computations. We propose an adaptive statistical approximation model for high-level resilience analysis that provides an opportunity to divide an iterative algorithm into exact and approximate iterations. We realize an energy-efficient accelerator based on a heterogeneous architecture, where the heterogeneity is introduced using accurate and approximate processing cores. Our proposed methodology exploits the error-resilience of the algorithm, where initial iterations are processed on approximate modules while the later ones on accurate modules. The proposed accelerator design does not increase the number of iterations as compared to that of an accurate counterpart and provides sufficient precision to converge to an acceptable solution. Our implementation using TSMC 40nm Low Power (TCBN40LP) technology shows 23% savings in electrical energy consumption.

Figures (12)

• Figure 1: Proposed high-level error resilience analysis model -- Adaptive-SAM. Our proposed model injects an error $\epsilon_\text{i}$ to an iteration of the dominant kernel $\text{K\_op}(i)$ if the randomized error and the approximate iterations flag ($\text{ER\_rand}(i)$ && $\text{ax\_iter\_flag}$) allow error injection to the iteration.
• Figure 2: StEFCal response for SAM analysis.
• Figure 3: Convergence (logarithmic scale) w.r.t the number of iterations; the algorithm converges at ER$=100\%$ when EP$=0$ (a) and (b). The algorithm does not converge when EP is raised to $0.1$ (c). For the simulations regarding EP$=0.1$ (c), EM has been varied from $5$ to $20$ with a step size of $5$ and ER has been varied from $20\%$ to $100\%$ with a step size of $20\%$.
• Figure 4: StEFCal response for Adaptive-SAM analysis.
• Figure 5: Our design methodology for an approximate Least Squares (LS) accelerator enables initial iterations to be processed on an approximate core (while the rest on an accurate core) to achieve an overall energy-efficiency.