Table 2.1: Comparison of different method of LFSR–based SNG
150 150
0
0.64 0.66 0.68 0.7 0.72 0.74
Classical LFSR approach
0.64 0.66 0.68 0.7 0.72 0.74 0.76
Multiple LFSR approach
0.66 0.68 0.7 0.72 0.74
Leap Ahead LFSR approach
Figure 2.6: Histogram of three approaches of LFSR–based SNG with the expected probability 0.7
Under such configuration, it can be shown in Fig.2.6 that from left–to–right there are no considerable differences in the distributions of three approaches around central value 0.7. The same conclusion when we consider the Empirical CDF function corresponding to each approach as shown in Fig.2.7. Moreover, Table 2.1 also shows a similar quality for all three method when the error is evaluated. Nevertheless, due to the results in this table, with a strict requirement in generating SN, Leap–Ahead architecture seems to be the best one playing as SNG based on LFSR.
In addition, it is theoretical to see that the classical LFSR method is not amenable for generating SN in parallel. Hence, we can conclude that with the nearly same quality of SN generation, multiple LFSRs and Leap–Ahead LFSR approaches are the good choices. However, using multiple LFSRs deals with the complexity in harware design, while Leap–Ahead architecture has only one LFSR. Consequently,
Leap–Ahead approach consumes less harware material than Multiple LFSRs one. Furthermore, Multi- ple LFSRs design has 16×32 cells need to be initialised at the beginning, while Leap–Ahead architecture
has only 32 cells, i.e, there are more slices for Multiple LFSRs method in innitial phase when implement
on FPGA platform. In conclusion, Leap–Ahead architecture will be a better selection than multiple LFSRs one not only in quality aspect, but also in low–cost evaluation.

CA–based SNG

\label{cabased-sng}
According to the analysis related to CA–based SNG in the above sections, we will implement both
single rule and mixed rule approaches under the parameters as follows:
Empirical CDF
\label{empirical-cdf}
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
x
\label{x}
Figure 2.7: Empirical CDFs of three approaches of LFSR–based SNG corresponding to the expected probability 0.7
4000
1200