Using Two-Dimensional Finite State Machine for Stochastic Computation

Stochastic computational elements, which perform computation based on stochastic bit streams, have several advantages compared to deterministic computational elements, such as high fault-tolerance and low hardware cost. Additionally, researchers have shown that a linear Finite State Machine (FSM) can be used to compute some functions stochastically, such as the exponentiation and tanh functions, more efficiently than combinational logic. However, we found that the functions that can be efficiently synthesized by the linear FSM in stochastic computing are very limited. In this paper, we propose a TwoDimensional (2D) FSM topology, which offers us more degrees of freedom, to resolve this issue. The analysis of the 2D FSM is given, and a general synthesis approach is demonstrated. Experimental results show that the proposed 2D FSM can be used to efficiently synthesize those functions which cannot be synthesized by the linear FSM. Compared to the deterministic implementations, the 2D FSM-based stochastic computational elements are much more fault-tolerant and have less area-delay products. Furthermore, compared to a previous combinational logic based synthesis approach, the proposed approach has less area-delay product with comparable fault-tolerance.