Analyzing and controlling accuracy in stochastic circuits

Stochastic computing (SC) is an approximate computing technique that represents data by probabilistic bit-streams called stochastic numbers (SNs). Arithmetic operations can be implemented at very low cost by means of SC. To achieve acceptable accuracy, interacting SNs must usually be statistically independent or uncorrelated. Correlation is poorly understood, however, and is a key problem in SC because of its impact on accuracy and the high cost of correlation-reducing logic. In this paper we analyze and quantify the role of correlation in stochastic circuit design. We use an algebraic framework based on probabilistic transfer matrices (PTMs) to analyze correlation-induced errors. We compare two systematic correlation-reducing methods, regeneration and isolation. Regeneration introduces new (pseudo) random sources to re-randomize SNs, while isolation uses delays (D flip-flops) to derive multiple independent SNs from a single random source. We present bounds on accuracy loss due to isolator insertion and compare its hardware cost to that of regeneration. We conclude that the isolation method can offer significant cost advantages in reducing correlation errors.