Stochastic Computing Implementation of Chaotic Systems
Abstract
:1. Introduction
2. Stochastic Computing Implementation of Analog Systems
2.1. Introduction to Stochastic Computing
2.2. Implementation of Basic Differential Equations
- Rewriting the equation in a form suited to SC. In the most basic case, this implies replacing all the additions by half additions: . Other, more complex operations may require a harder reworking of the equations to ensure all the operations can be implemented in SC in the [−1,1] or [0,1] range. For instance, in the case of implementing a division, one has to ensure that the result is always going to be in range, which may require an additional scaling and shifting of the variables involved.
- Scaling all the variables into the [−1,1] or [0,1] domains, since those are the values that can be dealt with in SC.
- Then, a final transformation ensures that all the modules of the coefficients in the equations are lower than 1. This is equivalent to a time scaling.
2.3. Basic Examples
2.3.1. Integrating a Constant (Twice)
2.3.2. A Simple Oscillator
3. Implementing Chaotic Systems in SC
3.1. The Shimizu-Morioka System
3.2. Equation Preparation
3.3. Implementation
3.4. Chaotic Evaluation
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AI | Artificial Intelligence |
B2S | Binary to Stochastic |
BEN | Binary Encoded Number(s) |
FFT | Fast Fourier Transform |
FPGA | Field Programmable Gate Array |
IoT | Internet of Things |
JTAG | Joint Test Action Group |
NF | Noise Figure |
RNG | Random Number Generator |
SC | Stochastic Computing |
SCN | Stochastic Computing Number |
SEN | Stochastic Encoded Number(s) |
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Order | Classical | SC |
---|---|---|
0.02112 | 0.03774 | |
−0.00487 | −0.00462 | |
−0.31142 | −0.29139 |
Algorithm | bits | Slices | LUTs |
---|---|---|---|
Vedic | 4 | 19 | 33 |
SC | 6 | 1 | 1/3 * |
Vedic | 16 | 346 | 622 |
SC | 22 | 1 | 1/3 * |
Vedic | 32 | 1427 | 2566 |
SC | 32 | 1 | 1/3 * |
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Camps, O.; Stavrinides, S.G.; Picos, R. Stochastic Computing Implementation of Chaotic Systems. Mathematics 2021, 9, 375. https://doi.org/10.3390/math9040375
Camps O, Stavrinides SG, Picos R. Stochastic Computing Implementation of Chaotic Systems. Mathematics. 2021; 9(4):375. https://doi.org/10.3390/math9040375
Chicago/Turabian StyleCamps, Oscar, Stavros G. Stavrinides, and Rodrigo Picos. 2021. "Stochastic Computing Implementation of Chaotic Systems" Mathematics 9, no. 4: 375. https://doi.org/10.3390/math9040375
APA StyleCamps, O., Stavrinides, S. G., & Picos, R. (2021). Stochastic Computing Implementation of Chaotic Systems. Mathematics, 9(4), 375. https://doi.org/10.3390/math9040375