Multiplexer-Majority Chains: Managing Correlation and Cost in Stochastic Number Generation

High-cost stochastic number generators (SNGs) are the main source of stochastic numbers (SNs) in stochastic computing. Interacting SNs must usually be uncorrelated for satisfactory results, but deliberate correlation can sometimes dramatically reduce area and/or improve accuracy. However, very little is known about the correlation behavior of SNGs. In this work, a core SNG component, its probability conversion circuit (PCC), is analyzed to reveal important tradeoffs between area, correlation, and accuracy. We show that PCCs of the weighted binary generator (WBG) type cannot consistently generate correlated bitstreams, which leads to inaccurate outputs for some designs. In contrast, comparator-based PCCs (CMPs) can generate highly correlated bitstreams but are about twice as large as WBGs. To overcome these area-correlation limitations, a novel class of PCCs called multiplexer majority chains (MMCs) is introduced. Some MMCs are area efficient like WBGs but can generate highly correlated SNs like CMPs and can reduce the area of a filtering circuit by 30% while sacrificing only 7% accuracy. The large influence of PCC design on circuit area and accuracy is explored and suggestions are made for selecting the best PCC based on a target system's correlation requirements.