Fast communication: Discrete-time chaotic systems synchronization performance under additive noise
TL;DR: Results are presented of a comparison between synchronization error due to additive Gaussian noise when the transmitter and receiver are implemented by single or coupled maps.
Abstract: In recent decades many articles have discussed the possibilities of chaos applied in communications. However, the vast majority consider in practical terms the ideal channel condition, which is clearly a restringing condition. Some papers show that when there is an additive noise, the synchronization error often disrupts communication. In this work, we present results of a comparison between synchronization error due to additive Gaussian noise when the transmitter and receiver are implemented by single or coupled maps.
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TL;DR: The obtained experimental results show the relevance of the idea of combining XBee (Zigbee or Wireless Fidelity) protocol, known for its high noise immunity, to secure hyperchaotic communications.
Abstract: In this paper, we propose and demonstrate experimentally a new wireless digital encryption hyperchaotic communication system based on radio frequency (RF) communication protocols for secure real-time data or image transmission. A reconfigurable hardware architecture is developed to ensure the interconnection between two field programmable gate array development platforms through XBee RF modules. To ensure the synchronization and encryption of data between the transmitter and the receiver, a feedback masking hyperchaotic synchronization technique based on a dynamic feedback modulation has been implemented to digitally synchronize the encrypter hyperchaotic systems. The obtained experimental results show the relevance of the idea of combining XBee (Zigbee or Wireless Fidelity) protocol, known for its high noise immunity, to secure hyperchaotic communications. In fact, we have recovered the information data or image correctly after real-time encrypted data or image transmission tests at a maximum distance (indoor range) of more than 30 m and with maximum digital modulation rate of 625,000 baud allowing a wireless encrypted video transmission rate of 25 images per second with a spatial resolution of 128 × 128 pixels. The obtained performance of the communication system is suitable for secure data or image transmissions in wireless sensor networks.
53 citations
Cites background or methods from "Fast communication: Discrete-time c..."
...Other authors proposed to improve the robustness of chaotic synchronization to channel noise [18], where a coupled lattice instead of coupled single maps is used to decrease the master-slave synchronization error....
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...digital modulation in the case of the transmission data rate of 250 kbps (the maximum serial interface data rate of the XBee Pro modules [18] allowed with a clk_out signal frequency equal to 250 kHz) with a distance frame value of N = 500 clock cycles, allowing signal captures....
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TL;DR: This paper succinctly describes techniques to counter the effects of finite bandwidth, additive noise and delay in the communication channel to make chaos-based communication systems attain lower levels of BER in non-ideal environments.
Abstract: Recently, many chaos-based communication systems have been proposed. They can present the many interesting properties of spread spectrum modulations. Besides, they can represent a low-cost increase in security. However, their major drawback is to have a Bit Error Rate (BER) general performance worse than their conventional counterparts. In this paper, we review some innovative techniques that can be used to make chaos-based communication systems attain lower levels of BER in non-ideal environments. In particular, we succinctly describe techniques to counter the effects of finite bandwidth, additive noise and delay in the communication channel. Although much research is necessary for chaos-based communication competing with conventional techniques, the presented results are auspicious.
50 citations
TL;DR: This work deduce analytical expressions for autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by a piecewise-linear map, with multiple segments.
Abstract: In recent decades, many studies with practical applications of chaotic signals in telecommunications and signal processing have been carried out. Although spectral analysis is of relevance in these areas, there are few analytical results concerning the spectral characterization of chaotic signals. In this work, we deduce analytical expressions for autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by a piecewise-linear map, with multiple segments. We present numerical simulations to confirm the theoretical results. HighlightsWe deduce the power spectral density and bandwidth of signals generated by a piecewise-linear map, with multiple segments.Numerical simulations are presented to confirm the theoretical results.Results generalize particular cases presented in the literature and can be useful in the analysis and synthesis of chaos-based communication systems.
15 citations
TL;DR: The proposed solution to the high channel noise sensibility problem of digital chaotic communications by avoiding disruption of the slave/receiver dynamics by injecting the driving signal is tested and validated through experimental realization of a wireless hyperchaotic communication system based on ZigBee communication protocol.
Abstract: An interesting and original solution to the high channel noise sensibility problem of digital chaotic communications is proposed. The solution idea consist of avoiding disruption of the slave/receiver dynamics by injecting the driving signal. To realize experimentally this pertinent idea, an FPGA-based hardware architecture is developed, flrstly to trigger the generation of the slave/receiver chaotic dynamics at each received data detection, and secondly to synchronize the driving signal with the slave generated chaotic signal for the demodulation operation. We have tested and validated the proposed solution through experimental realization of a wireless hyperchaotic communication system based on ZigBee communication protocol. Real-time results of experimental wireless communication tests are presented. The obtained results show the efiectiveness and the robustness of the proposed solution against real channel noise in digital chaotic
9 citations
Cites background from "Fast communication: Discrete-time c..."
...The authors in [12] investigate numerically an alternative model to decrease the masterslave synchronization error when there is additive white Gaussian noise between master and slave: using coupled lattices instead of coupled single maps....
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TL;DR: This work evaluates the performance in terms of Bit Error Rate (BER) of a binary communication system, based on chaotic synchronization, when white gaussian noise is added to the transmitted signal and proposes an encoding function that allows controlling the trade-off between how apparent is the message in the transmitted chaotic signal and BER performance.
Abstract: In recent decades, many papers describing communication systems based on chaotic signals have been published. However, their performance under non ideal conditions needs further investigation. This work evaluates the performance in terms of Bit Error Rate (BER) of a binary communication system, based on chaotic synchronization, when white gaussian noise is added to the transmitted signal. Furthermore, we propose an encoding function that allows controlling the trade-off between how apparent is the message in the transmitted chaotic signal and BER performance.
7 citations
References
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TL;DR: This chapter describes the linking of two chaotic systems with a common signal or signals and highlights that when the signs of the Lyapunov exponents for the subsystems are all negative the systems are synchronized.
Abstract: Certain subsystems of nonlinear, chaotic systems can be made to synchronize by linking them with common signals. The criterion for this is the sign of the sub-Lyapunov exponents. We apply these ideas to a real set of synchronizing chaotic circuits.
9,201 citations
Book•
01 Jan 1994
TL;DR: The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter, and the progression through period-doubling bifurcations to the onset of chaos is considered.
Abstract: We explore several basic aspects of chaos, chaotic systems, and non-linear dynamics through three different setups. The logistic map, a canonical one-dimensional system exhibiting surprisingly complex and aperiodic behavior, is modeled as a function of its chaotic parameter. We consider maps of its phase space, and the progression through period-doubling bifurcations to the onset of chaos. The Feigenbaum ratio of successive bifurcation periods is estimated at 4.674, in good agreement with the accepted value. The Liapunov exponent, governing the exponential growth of small perturbations in chaotic systems, is calculated and its fractal structure compared to the corresponding bifurcation diagram for the logistic map. Using a non-linear p-n junction circuit we analyze the return maps and power spectrums of the resulting time series at various types of system behavior. Similarly, an electronic analog to a ball bouncing on a vertically driven table provides insight into real-world applications of chaotic motion. For both systems we calculate the fractal information dimension and compare with theoretical behavior for dissipative versus Hamiltonian systems. Subject headings: non-linear dynamics; non-linear dynamical systems; fractal dimension; chaos; strange attractors; logistic map
5,372 citations
TL;DR: This book discusses Chaos, Fractals, and Dynamics, and the Importance of Being Nonlinear in a Dynamical View of the World, which aims to clarify the role of Chaos in the world the authors live in.
Abstract: Preface 1. Overview 1.0 Chaos, Fractals, and Dynamics 1.1 Capsule History of Dynamics 1.2 The Importance of Being Nonlinear 1.3 A Dynamical View of the World PART I. ONE-DIMENSIONAL FLOWS 2. Flows on the Line 2.0 Introduction 2.1 A Geometric Way of Thinking 2.2 Fixed Points and Stability 2.3 Population Growth 2.4 Linear Stability Analysis 2.5 Existence and Uniqueness 2.6 Impossibility of Oscillations 2.7 Potentials 2.8 Solving Equations on the Computer Exercises 3. Bifurcations 3.0 Introduction 3.1 Saddle-Node Bifurcation 3.2 Transcritical Bifurcation 3.3 Laser Threshold 3.4 Pitchfork Bifurcation 3.5 Overdamped Bead on a Rotating Hoop 3.6 Imperfect Bifurcations and Catastrophes 3.7 Insect Outbreak Exercises 4. Flows on the Circle 4.0 Introduction 4.1 Examples and Definitions 4.2 Uniform Oscillator 4.3 Nonuniform Oscillator 4.4 Overdamped Pendulum 4.5 Fireflies 4.6 Superconducting Josephson Junctions Exercises PART II. TWO-DIMENSIONAL FLOWS 5. Linear Systems 5.0 Introduction 5.1 Definitions and Examples 5.2 Classification of Linear Systems 5.3 Love Affairs Exercises 6. Phase Plane 6.0 Introduction 6.1 Phase Portraits 6.2 Existence, Uniqueness, and Topological Consequences 6.3 Fixed Points and Linearization 6.4 Rabbits versus Sheep 6.5 Conservative Systems 6.6 Reversible Systems 6.7 Pendulum 6.8 Index Theory Exercises 7. Limit Cycles 7.0 Introduction 7.1 Examples 7.2 Ruling Out Closed Orbits 7.3 Poincare-Bendixson Theorem 7.4 Lienard Systems 7.5 Relaxation Oscillators 7.6 Weakly Nonlinear Oscillators Exercises 8. Bifurcations Revisited 8.0 Introduction 8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations 8.2 Hopf Bifurcations 8.3 Oscillating Chemical Reactions 8.4 Global Bifurcations of Cycles 8.5 Hysteresis in the Driven Pendulum and Josephson Junction 8.6 Coupled Oscillators and Quasiperiodicity 8.7 Poincare Maps Exercises PART III. CHAOS 9. Lorenz Equations 9.0 Introduction 9.1 A Chaotic Waterwheel 9.2 Simple Properties of the Lorenz Equations 9.3 Chaos on a Strange Attractor 9.4 Lorenz Map 9.5 Exploring Parameter Space 9.6 Using Chaos to Send Secret Messages Exercises 10. One-Dimensional Maps 10.0 Introduction 10.1 Fixed Points and Cobwebs 10.2 Logistic Map: Numerics 10.3 Logistic Map: Analysis 10.4 Periodic Windows 10.5 Liapunov Exponent 10.6 Universality and Experiments 10.7 Renormalization Exercises 11. Fractals 11.0 Introduction 11.1 Countable and Uncountable Sets 11.2 Cantor Set 11.3 Dimension of Self-Similar Fractals 11.4 Box Dimension 11.5 Pointwise and Correlation Dimensions Exercises 12. Strange Attractors 12.0 Introductions 12.1 The Simplest Examples 12.2 Henon Map 12.3 Rossler System 12.4 Chemical Chaos and Attractor Reconstruction 12.5 Forced Double-Well Oscillator Exercises Answers to Selected Exercises References Author Index Subject Index
2,949 citations
Book•
07 Nov 1996
TL;DR: One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.
Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.
1,924 citations
Additional excerpts
...Contents lists available at ScienceDirect Signal Processing 0165-16 doi:10.1 Cor E-m batista@ journal homepage: www.elsevier.com/locate/sigpro Fast communication Discrete-time chaotic systems synchronization performance under additive noise M. Eisencraft a, , A.M. Batista b, a Centro de Engenharia,…...
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TL;DR: The authors describe the conditions necessary for synchronizing a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem by sending signals from the Chaos Junction.
Abstract: The authors describe the conditions necessary for synchronizing a subsystem of one chaotic system with a separate chaotic system by sending a signal from the chaotic system to the subsystem. The general scheme for creating synchronizing systems is to take a nonlinear system, duplicate some subsystem of this system, and drive the duplicate and the original subsystem with signals from the unduplicated part. This is a generalization of driving or forcing a system. The process can be visualized with ordinary differential equations. The authors have build a simple circuit based on chaotic circuits described by R. W. Newcomb et al. (1983, 1986), and they use this circuit to demonstrate this chaotic synchronization. >
1,234 citations
Additional excerpts
...& 2011 Published by Elsevier B.V....
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