Timing error statistics for energy-efficient robust DSP systems

This paper makes a case for developing statistical timing error models of DSP kernels implemented in nanoscale circuit fabrics. Recently, stochastic computation techniques have been proposed [1], [2], [3], where the explicit use of error-statistics in system design has been shown to significantly enhance robustness and energy-efficiency. However, obtaining the error statistics at different process, voltage, and temperature (PVT) corners is hard. This paper: 1) proposes a simple additive error model for timing errors in arithmetic computations due PVT variations, 2) analyzes the relationship between error statistics and parameters, specifically the input statistics, and 3) presents a characterization methodology to obtain the proposed model parameters and thus enabling efficient implementations of emerging stochastic computing techniques. Key results include the following observations: 1) the output error statistics is a weak function of input statistics, and 2) the output error statistics depends upon the one's probability profile of the input word. These observations enable a one-time off-line statistical error characterization of DSP kernels similar to delay and power characterization done presently for standard cells and IP cores. The proposed error model is derived for a number of DSP kernels in a commercial 45nm CMOS process.