Polynomial Computation Using Unipolar Stochastic Logic and Correlation Technique
Abstract
This article addresses polynomial computation with unipolar stochastic logic by exploiting correlation between the bit-streams. The AND-OR, double-NAND, OR-AND and double-NOR circuits are presented for polynomials with all positive coefficients whose sum is less than or equal to one by mathematically analyzing the joint probability distribution of coefficient bit-streams. The NAND-AND expansion is also developed for polynomials with alternatively positive and negative coefficients whose absolute values are decreasing by applying the same idea. Unlike the original methods with multiple uncorrelated random number sources (RNSs) for coefficient bit-stream generation, the presented methods only require a single RNS. Since the RNSs take up huge hardware resource in stochastic circuits, the proposed RNS-sharing techniques for polynomial computation result in a significant reduction of hardware complexity. For the factorization technique in the general polynomials, this paper enhances the original stochastic designs for the second-order polynomial and further presents the simple correlation-dependent circuits. Results show that the proposed architectures are superior to the previous ones by reducing the total number of RNSs.