Compact and accurate digital filters based on stochastic computing

Stochastic computing (SC), which is an approximate computation with probabilities, has attracted attention as an alternative to deterministic computing. In this paper, we discuss a design method for compact and accurate digital filters based on SC. Such filter designs are widely used for various purposes, such as image and signal processing and machine learning. Our design method involves two techniques. One is sharing random number sources with several stochastic number generators to reduce the areas required by these generators. Clarifying the influence of the correlation around multiplexers (MUXs) on computation accuracy and utilizing circular shifts of the output of random number sources, we can reduce the number of random number sources for a digital filter without losing accuracy. The other technique is to construct a MUX tree, which is the principal part of an SC-based filter. We formulate the correlation-induced errors produced by the MUX tree, and then propose an algorithm for constructing an optimum MUX tree to minimize the error. Experimental results show that the proposed design method can derive compact (approximately 70 percent area reduction) SC-based filters that retain high accuracy.