Exploiting correlation in stochastic circuit design

Stochastic computing (SC) is a re-emerging computing paradigm which enables ultra-low power and massive parallelism in important applications like real-time image processing. It is characterized by its use of pseudo-random numbers implemented by 0-1 sequences called stochastic numbers (SNs) and interpreted as probabilities. Accuracy is usually assumed to depend on the interacting SNs being highly independent or uncorrelated in a loosely specified way. This paper introduces a new and rigorous SC correlation (SCC) measure for SNs, and shows that, contrary to intuition, correlation can be exploited as a resource in SC design. We propose a general framework for analyzing and designing combinational circuits with correlated inputs, and demonstrate that such circuits can be significantly more efficient and more accurate than traditional SC circuits. We also provide a method of analyzing stochastic sequential circuits, which tend to have inherently correlated state variables and have proven very hard to analyze.