This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 1 Computation on Stochastic Bit Streams Digit

Abstract — Maintaining the reliability of integrated circuits as transistor sizes continue to shrink to nanoscale dimensions is a significant looming challenge for the industry. Computation on stochastic bit streams, which could replace conventional deterministic computation based on a binary radix, allows similar computation to be performed more reliably and often with less hardware area. Prior work discussed a variety of specific stochastic computational elements (SCEs) for applications such as artificial neural networks and control systems. Recently, very promising new SCEs have been developed based on finite-state machines (FSMs). In this paper, we introduce new SCEs based on FSMs for the task of digital image processing. We present five digital image processing algorithms as case studies of practical applications of the technique. We compare the error tolerance, hardware area, and latency of stochastic implementations to those of conventional deterministic implementations using binary radix encoding. We also provide a rigorous analysis of a particular function, namely the stochastic linear gain function, which had only been validated experimentally in prior work. Index Terms — Digital image processing, fault tolerance, finite state machine (FSM), stochastic computing. I