A Regression-Based Method to Synthesize Complex Arithmetic Computations on Stochastic Streams

Arash Ardakani, Amir Ardakani, Warren J. Gross

Abstract: In stochastic computing, values are represented as sequences of random bits and arithmetic computations are computed on the bit streams. Since bit-wise operations are performed on random bit streams, stochastic computing offers low-cost error-tolerant architectures for its hardware implementations. In stochastic computing, complex arithmetic operations can be computed using linear finite state machines (FSMs). However, the synthesis of a linear FSM for a given target function is nontrivial. In this paper, we exploit linear regression and demonstrate a general approach to synthesize linear FSMs for stochastic computations. We show that our approach outperforms traditional numerical synthesis methods in terms of mean-squared error. We also demonstrate that fault-tolerance of FSMs synthesized using linear regression can be improved by injecting noise during the synthesis phase, allowing the synthesized functions to tolerate up to 35% of random bit flips.