Output
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
Eaverage =
.m
i=1
.n
j=1 |