Digital Signal Processing Reference
In-Depth Information
frequencies (about 10 MHz) an error rate of 1 % and a bandwidth of approximately
100 Hz can be achieved.
However, the moderate computing accuracy and speed are quite acceptable for
many applications and the advantages of stochastic computing may well outnum-
ber its drawbacks. When this new concept of computation was first proposed, it
was strongly recommended for applications in the field of real-time automatic
control and the simulation of large complex systems. It was predicted that with
advances in large-scale integrated circuit manufacturing, stochastic computing
would be widely and successfully employed to solve many important problems.
However, these predictions did not come true. Developments in microprocessor
technology allowed the design of more efficient computing systems, including
multiprocessor systems. Stochastic computers could not compete and interest in
stochastic computing gradually declined. However, the fact still remains that com-
putation of stochastically represented variables can be performed in an extremely
simple and economic way.
The layout and interconnections of computing elements in stochastic comput-
ers depend on the particular computations to be carried out. Several stochastic
computer hardware mapping schemes are possible. The most commonly used are
based on a single-line unipolar representation of the variables, which are always
positive (or always negative). This scheme leads to the simplest hardware con-
figurations of computing elements, although these elements are still quite simple
even when other mapping schemes are implemented.
Multiplication is one of the most basic and frequently used computing opera-
tions. The complexity of the hardware performing this operation is an important
issue for any type of computer. In the case of stochastic computers, the variables,
represented by stochastic quantities, may be multiplied in an extremely simple
way. For example, only a single logic AND gate is required for multiplying two
unipolar variables represented by corresponding stochastic bit streams.
Many specific stochastic elements have been developed over the years. How-
ever, only relatively few types of elements are actually needed to build a stochastic
computer. Such a computer is basically comprised of a large number of simple
and cheap multipliers and summers.
The original signals to be processed by this kind of computer first have to
be converted into stochastic bit streams. This has to be done whether the input
signals are analog or digital. Therefore at least two types of converters are needed:
analog-stochastic and digital-stochastic converters.
It is easy to see that a randomized one-bit quantizer can be used for conversion
of an analog unipolar signal to a stochastic bit stream. If the signal at the input of
such a converter varies sufficiently slowly, the obtained bit stream would represent
