Output
Figure 2.22: Generating stochastic constant using LFSR
Empirical
CDF\label{empirical-cdf-1}
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
x\label{x-1}
Figure 2.23: Emperical CDF function of SNGs using comparator and SNG
based on Markov chain
Finally, because of the reduction in number of PRNGs, we can mage a
comparison between the SNG based Markov chain and other approaches in
the first category. It can be shown in
Fig.2.23 that the Markov chain
based SNG has a better performance than others, except SNG relied on CA
rule 30. The good features of FSM is once again illustrated in this
comparison. Besides, the number of random source (the best one is 3 as
discussed in section 2.3.4) in this
method is greater than others using comparator, it can be consequently
its drawback. However, this value is a design parameter, i.e., the
hardware cost can be therefore controlled when considering Markov chain
in generating SN.
Chapter
3
Stochastic Operators
Arithmetic operators play an important role in designing an SC
architecture. They can either be the operators in
[9],
[4] which was implemented very
simply with basic logic elements or the others in
[15],
[4],
[17] which are more complicated
using Finite State Machines (FSMs). In this chapter, two groups of
Stochastic operators (SOs) will be systematically described and
analyzed:
-
SOs based on combinational logic: multiplication, scaled addition,
scaled subtraction operators;
-
SOs relied on sequential logic: exponentiation, tanh, absolute value,
exponentiation with an absolute value functions.
These computational elements will be investigated effectively in lots of
applications using SC, such as: digital filter, image processing,
neutral network. Because of the performing of complete analog com-
puting functions, SC has proved its capability as an alternative choice
to conventional real arithmetic.
-
Combinational
logic based
SOs
\label{combinational-logic-based-sos}
-
Stochastic
Multiplication
\label{stochastic-multiplication}
p1 = 01010101 (1/2)
p = 01000000 (1/8)
p1 = 01010000
(P = 1/4, N = -1/2)
p = 10101111
out
out