A Markov Chain Framework for Modeling the Statistical Properties of Stochastic Computing Finite-State Machines

A general methodology to derive analytically the statistical properties of stochastic computing finite-state machines (SFSMs) is introduced. The SFSMs, expressed as Moore ones, are modeled using Markov Chains (MCs), enabling the derivation in closed form of their output sequences’ statistical properties, including their expected value, their auto- and cross-correlation, their auto- and cross-covariance, their variance and standard deviation as well as their mean squared error. An MC overflow/underflow probability model accompanies the methodology, allowing to calculate analytically the expected number of steps before overflows/underflows, setting the guidelines to select the register’s size that reduces erroneous bits originating from them. In the proposed methodology both the input sequence length and the number of the SFSMs’ states are considered as parameters, accelerating the overall design procedure as the necessity for multiple time-consuming numerical simulations is eliminated. The proposed methodology’s accurate modeling capabilities are demonstrated with its application in two SFSMs selected from the stochastic computing literature, while comparisons with the numerical experiments justify its correctness.