IEEE Circuits and Systems Magazine - Q3 2020 - 19

Introduction
to Dynamic Stochastic
Computing

©ISTOCKPHOTO.COM/LOOPS7

Feature

Siting Liu, Warren J. Gross, and Jie Han

Abstract
Stochastic computing (SC) is an old but reviving computing paradigm for its simple data path that can perform various arithmetic
operations. It allows for low power implementation, which would
otherwise be complex using the conventional positional binary
coding. In SC, a number is encoded by a random bit stream of
'0's and '1's with an equal weight for every bit. However, a long bit
stream is usually required to achieve a high accuracy. This requirement inevitably incurs a long latency and high energy consumption
in an SC system. In this article, we present a new type of stochastic
computing that uses dynamically variable bit streams, which is,
therefore, referred to as dynamic stochastic computing (DSC). In
DSC, a random bit is used to encode a single value from a digital
signal. A sequence of such random bits is referred to as a dynamic
stochastic sequence. Using a stochastic integrator, DSC is well
suited for implementing accumulation-based iterative algorithms
such as numerical integration and gradient descent. The underlying mathematical models are formulated for functional analysis
and error estimation. A DSC system features a higher energy efficiency than conventional computing using a fixed-point representation with a power consumption as low as conventional SC. It is
potentially useful in a broad spectrum of applications including signal processing, numerical integration and machine learning.
Digital Object Identifier 10.1109/MCAS.2020.3005483
Date of current version: 12 August 2020

THIRD QUARTER 2020

I. Introduction
s an unconventional computing paradigm, stochastic computing (SC) operates on numbers encoded
by sequences of random '0's and '1's [1]. The probability of a '1' in the stochastic sequence is then used to
encode a number. The datapath of a typical SC system
consists of three major components: stochastic number
generators (SNGs), stochastic circuits and probability estimators (PEs), as shown in Fig. 1. Complex computation
can be performed by the stochastic circuits in relatively
simple bit-wise operations, while the SNG array and PEs
are used to convert numbers between the conventional
binary representation and stochastic encoding. SC has
been studied for decades for its relatively simple logic,
low power consumption, an inherent resilience to bit-flip
errors and biological plausibility.
In a stochastic sequence, a number, x, can be simply
encoded as the probability of a '1' or, approximately, as
the ratio of the number of '1's in the total number of bits.
An inverter then computes 1-x for an input sequence encoding x. For two independent input sequences encoding
x and y, an AND gate outputs a '1' when both the input bits

IEEE CIRCUITS AND SYSTEMS MAGAZINE

http://www.ISTOCKPHOTO.COM/LOOPS7

IEEE Circuits and Systems Magazine - Q3 2020

Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q3 2020