p = f (y)dy. (1.1)
−∞
In this case, our random source is considered as Uniform
distribution [1] in the
interval [0, 1], hence, the received probability will be
x as expected.
The random source plays the most important role in SNG, because without
a good randomness at the beginning, there is no SN. Moreover, a problem
must be noticed is that a random source is difficultly achieved in
experiment, therefore, the pseudo–random source or pseudo–random
number generator (PRNG) becomes a practical solution. Linear
Feedback Shift Register (LFSR) has been recommended in widely SC system
for random number generation
[9],
[19],
[4],
[24],
[13]. Besides, Cellula
Automata was equally considered in
[4],
[11],
[22],
[7] as a good solution for
PRNG.
The SNGs without using comparator was early proposed in
[9],
[4],
[12]. In these designs, the
basic logic elements, such as AND, OR, NOT gates and Multiplexer
(MUX), were used instead of the comparator to generate the stochastic
constants in SC with a high accuracy. Recently, a general synthesis
method to design Finite State Machines (FSMs) for generating SN was
developped in [21] with the
improvement comparing to previous works.
Furthermore, each SNG provides a specific probability, hence it is
problematic when the application requires many probabilities. Since on
the one hand, it is expensive to generate directly all required
probabilities from the random sources, on the other hand, it takes time
for this process. Consequently, a synthesis method was proposed in
[20] as a solution for this
problem. The aim of this approach is to synthesize combinational logic
that generates the expected probability from a specified source.
However, this method is successful in considering the input
probabilities being exact and independent. For that reason, there will
be a lot of study forcusing on this problem of SNG in future work.