Figure 4.13: Soft error injection in the implementation of an 2–input
operator
same way. From the different sources, the soft errors have an effect on
the inputs and output through the XOR gates as follows: at each clock
cycle, if the error signal is equal to 1, the corresponding original
signal: Input 1, Input 2, Output will be changed;
there is no influence, elsewhere. In this architecture, the soft error
sources is designed as one described in
[16] which is also interpreted
as the SNGs that generated the errors with the given ratios. In this
work, we use CA rule 30 based PRNGs in those error sources instead of
LFSRs. This method will be applied to the operator in conventional
computing (adder/subtractor, multiplier,…) as well as ones in SC (AND
gate, MUX, FSM–stochastic elements,…) to make a comparison in
fault–tolorant capacity between two computing approaches.
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Soft error ratio
Figure 4.14: Error comparison of the implemention of the multiplier
between Stochastic and Conventional computing in case of having the
injected soft error
As an example, we implement the multiplier of two numbers in
conventional computing, and corre- sponding to this operator, an 2–AND
gate is also carried out in SC. In each case of error injection, the
difference of the received results compared with the conventional
implementation in case of non–error injection is calculated. In
addition, in this simulation, different ratios of the soft error from 0
to 0.7 will be considered. It can be seen in
Fig.4.14 that the output error
increases when the soft error ratio increases and the error in case of
using SC is considerably smaller than one when using the conven- tional
approach. Besides, it can be see that the curves in this figure are
close to the linear equation of
(a) error ratio 0.01 (b)
error ratio 0.05 (c) error ratio 0.1 (d) error ratio
0.15 (e) error ratio 0.2
Figure 4.15: Evaluate the fault–tolerant capacity of SC (upper row)
compared to conventional computing (lower row) in condition of injecting
different soft error ratios
form y = ax + b, where the constant a
determines the slope or gradient of the line, and the
constant
b define the point at which the line crosses the vertical axis.
According to the obtained results, we can approximately have the slope
in SC aSC ≈ 0.14 and the slope in the conventional
computing aCC ≈ 0.64. It can be therefore concluded that
the conventional implementation is more sensitive
with the injected soft error than SC, i.e., SC is quitely stable before
the injection of soft error during
processing. By
Now, we continue considering the faul–tolerant capacity of SC in noise
reduction based on median filter. In this implemetation, stochastic
sequence of length 1024 will be employed. It can be shown in
Fig.4.15 that with the same soft
error ratio, SC ensures the performance of noise reduction better
than conventional one. Besides, by considering the input image with the
size of m × n, the average
error Eaverage is given as