Understanding variance propagation in stochastic computing systems

Stochastic arithmetic provide several benefits over traditional computing method such as high fault tolerance, simple hardware implementation, low hardware area. In order to increase accuracy of error analysis and improve method of performance evaluation for stochastic computing systems, a new variance transfer function for stochastic computing systems based on combinational logic is proposed in this work. The transfer function is proved by a new mathematical method: hypergeometric decomposition, which makes stochastic computing theory more perfect and reliable. According to the variance transfer function, several measurements based on variance are developed to evaluate performance between different stochastic computing algorithms. By comparing this method with traditional bit-level simulation method, variance measurements are proved to be less time consumption, more comprehensive, and more effective to evaluate and understand stochastic computing systems.