2.4 Comparison and conclusion

\label{comparison-and-conclusion}
According to the above results, it can be seen that both groups perform the good quality in generating SNs. They generate SNs which are close to the expected ones. However, there are the noticeable differences between these two groups of SNGs. In considering that we have the ideal PRNGs to employ in SNGs, the first group use only one PRNG then through the comparator one bit is generated at each
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0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75
Figure 2.21: Histogram and statistic parameters of the output value when using FSM to generate the expected probability 0.7
clock cycle. Meanwhile, the second one (except the SNGs based on Markov chain and LFSR) must employ more than two PRNG to produce the desired probability. The SNGs using comparator therefore consume less hardware than the first one. Besides, the variable probability converter and digital to stochastic converter have the distribution of the output values that are closer to the expected value in comparison with that of SNGs in the first group. Consequently, there are the trade–off between the hardware cost and the accuracy in selecting an amenable SNG between two categories.
About the LFSR–based binary to stochastic converter, this approach is firsly to generate the stochastic constant. When consider this one, LFSR must be used in condition of maximum length to achieve the exact results. This can be considered as a good idea for constants in SC. Besides, in this work, we propose another approach using LFSR to generate the stochastic constant which is shown in Fig.2.22. In this configuration, an n–stages LFSR is employed, however, the feedback path is a multiplexer instead of an XOR gate. In addition, the initial state of LFSR is fed by an SNG which generates a bit sequence of length n representing the expected probability p. The behavior of this architecture can be explained as follows. Each bit in LFSR has the probability p of being logic 1, therefore, bit in the feedback path or bit in the first tap pfb has a probability given as
1 1
pfb = n − 1 (p + … + p) = n − 1 (n − 1)p = p. (2.19)
Hence, after a right–shift event is executed, each bit in LFSR still has a probability p. Based on this fact, a SN of length N bits can be obtained after N clock cycles. However, the problem is that after a number of iteration, the accuracy will be degraded. We consequently reinitialise our LFSR to obtain the expected stochastic constant. If we can maintain the degradation in this such design in the future work, it might be a good stochastic constant generator.