On the Functions Realized by Stochastic Computing Circuits

Stochastic computing (SC) employs conventional logic circuits to implement analog-style arithmetic functions acting on digital bit-streams. It exploits the advantages of analog computation -powerful basic operations, high operating speed, and error tolerance- in important applications such as sensory image processing and neuromorphic systems. At the same time, SC exhibits the analog drawbacks of low precision and complex underlying behavior. Although studied since the 1960s, many of SC"s fundamental properties are not well known or well understood. This paper presents, in a uniform manner and notation, what is known about the relations between the logical and stochastic behavior of stochastic circuits. It also considers how correlation among input bit-streams and the presence of memory elements influences stochastic behavior. Some related research challenges posed by SC are also discussed.