Nonscaling Adders and Subtracters for Stochastic Computing Using Markov Chains

This work presents adder and subtracter architectures for stochastic computing (SC). In contrast to standard approaches, the result of their operation is nonscaling, i.e., $X\,\pm \,Y$ , and this is achieved via a deterministic operation based on a counting process. These properties result in an improved tradeoff between accuracy and stochastic sequence length, fast convergence, and the potential for cascaded, scale-dependent (e.g., nonlinear) stochastic computations providing with flexibility on the design level. The architectures are modeled using Markov chains (MCs) allowing for detailed understanding of their proper operation supported with analytical derivations. Using modified MC models, the adder and subtracter’s internal register size is analytically calculated providing guidelines for its optimal size selection based on accuracy requirements and stochastic input sequences lengths. Both architectures are simulated in MATLAB and are designed in Synopsys to compare their performance to that of existing ones in terms of computational accuracy and hardware resources. Finally, to demonstrate the adder’s efficacy, we use it as a building block to realize a $3 \times 3$ convolution kernel and then perform a standard digital image processing task. The results are compared to those achieved using adder architectures from the SC literature.