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
800
700
600
500
400
300
200
100
0
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
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.