Output
Figure 2.22: Generating stochastic constant using LFSR
Empirical CDF\label{empirical-cdf-1}
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 0.07
x\label{x-1}
Figure 2.23: Emperical CDF function of SNGs using comparator and SNG based on Markov chain
Finally, because of the reduction in number of PRNGs, we can mage a comparison between the SNG based Markov chain and other approaches in the first category. It can be shown in Fig.2.23 that the Markov chain based SNG has a better performance than others, except SNG relied on CA rule 30. The good features of FSM is once again illustrated in this comparison. Besides, the number of random source (the best one is 3 as discussed in section 2.3.4) in this method is greater than others using comparator, it can be consequently its drawback. However, this value is a design parameter, i.e., the hardware cost can be therefore controlled when considering Markov chain in generating SN.
Chapter 3
Stochastic Operators
Arithmetic operators play an important role in designing an SC architecture. They can either be the operators in [9], [4] which was implemented very simply with basic logic elements or the others in [15], [4], [17] which are more complicated using Finite State Machines (FSMs). In this chapter, two groups of Stochastic operators (SOs) will be systematically described and analyzed:
These computational elements will be investigated effectively in lots of applications using SC, such as: digital filter, image processing, neutral network. Because of the performing of complete analog com- puting functions, SC has proved its capability as an alternative choice to conventional real arithmetic.
  1. Combinational logic based SOs

    \label{combinational-logic-based-sos}
    1. Stochastic Multiplication

      \label{stochastic-multiplication}
    p1 = 01010101 (1/2)
    p = 01000000 (1/8)
    p1 = 01010000
    (P = 1/4, N = -1/2)
    p = 10101111
    out
    out