Impact of Autocorrelation on Stochastic Circuit Accuracy

Stochastic computing (SC) with pseudo-random numbers offers the prospect of significant chip area and energy savings for large-scale applications such as neural networks. Because of SC's inherent stochasticity, all phenomena affecting accuracy must be carefully analyzed and controlled. This work addresses a fundamental error source, autocorrelation, which although recognized, has largely been neglected in the SC context. We observe that autocorrelation occurs in all types of stochastic circuits and has a major impact on the accuracy of sequential stochastic circuits. We present a methodology for analyzing autocorrelation and apply it to two broad SC circuit types: counter-based and shift-register based. We demonstrate the use of Markov chain theory to estimate autocorrelation errors in stochastic circuits. We also present an algorithm SANG for efficiently generating stochastic numbers that have prescribed autocorrelation and numerical values. SANG greatly aids the simulation of autocorrelation effects in SC.