Minimizing Error of Stochastic Computation through Linear Transformation

Stochastic computation is an unconventional computational paradigm that uses ordinary digital circuits to operate on stochastic bit streams, where signal value is encoded as the probability of ones in a stream. It is highly tolerant of soft errors and enables complex arithmetic operations to be implemented with simple circuitry. Prior research has proposed a method to synthesize stochastic computing circuits to implement arbitrary arithmetic functions by approximating them via Bernstein polynomials. However, for some functions, the method cannot find Bernstein polynomials that approximate them closely enough, thus causing a large computation error. In this work, we explore linear transformation on a target function to reduce the approximation error. We propose a method to find the optimal linear transformation parameters to minimize the overall error of the stochastic implementation. Experimental results demonstrated the effectiveness of our method in reducing the computation error and the circuit area.