Table 2.2: Comparison of two methods of CA–based SNG: single rule and mixed rule
one (in blue) where there is a ristrict requirement to the error. This fact can be explained by the dynamic change in selection appropriate rule for calculating the output of mixed rule CA, i.e., there are not only the randomness in inherent feature of CA but also an additional randomizing effect in rule decision. This result is suitable due to the comparison between PRNGs which were introduced in [11]. In addition, this Fig.2.9 once again illustrates the outstanding quality in using one–dimensional CA corresponds to rule 30.

Comparison between LFSR–based and CA–based SNGs

\label{comparison-between-lfsrbased-and-cabased-sngs}
Now we consider all five above approaches to make a comparison. Fig.2.10 shows that CA–based SNGs produce SNs with a higher quality compared to LFSR–based SNGs. When error is less than 0.005 mixed rule CA can be seen similar to LFSR–based approach, however, at the other position of error, it give a considerable improvement comparing to others. This figure also gives the best performance belonging to single rule 30 that we saw in the previous section.
LFSR has a strong correlation between its generated partterns due to the shifting of data, while CA evolution bases on its own state, the neighbors states and rules. CA–based approaches will consequently give a better performance in comparison with ones relied on LFSR. Nevertheless, an LFSR can be implemented using only a few gates, i.g. XOR gates, whereas an CA needs at least one XOR gate for each cell. From this fact, it can be visually seen that the higher area overhead regarding to carrying out CA compared to implemtation of LFSR. Therefore, there are the trade–off in selecting CA or LFSR in our implemntation, i.e., the compromission between accuracy and hardware cost.
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Figure 2.10: Empirical CDF of five SNGs relied on LFSR and CA