A digital bandlimited chaos-based communication system

In this work we propose a methodology to design communication systems based on the topology of chaotic attractors. This methodology is based on the connection between the chaotic flux generated by the system equations and a state diagram, defined by a Poincaré section. We define a map between binary sequences and transitions on the diagram state. These transitions are performed by chaotic curves that connect subregions of the Poincaré section. The chaotic signals are transmitted over a additive white Gaussian noise channel. We demonstrate that chaotic communication systems based on Lorenz attractor have superior performance than communication systems based on Rössler attractor. Keywords— Chaos based communications, topology of chaotic dynamical systems, symbolic dynamics, chaos control, error probability.

Sistemas de Comunicação Digital Baseados no Atrator Caótico de Lorenz

In this paper, we have designed and proposed a new improved Logistic map (ILM) which enhances the performance of the standard Logistic map (SLM) in terms of higher Lyapunov exponent and steady chaotic behavior. In standard map, the control parameter is limited and should be close to 4 to exhibit chaos. Additionally, in some specific region called as islands of stability, the system behaves non-chaotic. However, for the improved one, the control parameter is not limited to a finite value for the system to be in chaos state and provides chaotic behavior all the time. Firstly, we have designed a new chaotic map and modeled it by using Xilinx block sets in Matlab/Simulink environment. Then, we have realized the ILM through hardware-co simulation on FPGA (Field programmable gate array) for practical applications.

An efficient method to improve the Logistic map: Design and implementation

In this paper, we proposed the FPGA based digital implementation of synchronization methodology for 6-D chaotic systems via nonlinear feedback adaptive control technique. We derived new results for the adaptive controllers and the parameter update laws based on Lyapunov stability theory to achieve the synchronization between identical 6-D chaotic systems. Since the digitization of chaotic synchronization is necessary for digital communication, the proposed adaptive synchronization methodology is implemented in digital circuits based on Field Programmable Gate Array chip. The digital chaotic signal also generated using MATLAB simulink and Xilinx System Generator technology. The numerical simulation and FPGA outputs are used to prove the robustness and effectiveness of our proposed methodology.

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FPGA Based Digital Implementation of Adaptive Synchronization Methodology for 6-D Chaotic System

In recent decades, several chaos-based communication systems have been proposed. Many of them use a function to encode a message into a chaotic signal, which is characterized as wideband. Since every transmission channel is bandlimited in nature, it is necessary to determine and to control the spectrum of the chaotic signal transmitted by this system. This way, a bandlimited chaos-based communication system was recently proposed using digital filters and chaotic synchronization. These filters, inserted in the communication system, modify the original chaotic generator system, becoming necessary to study how their insertion affect chaotic synchronization. In this work, we present an analysis of this discrete-time chaos-based digital communication system considering an additive white Gaussian noise channel. The synchronization conditions of this system is analytically obtained, through a theorem, for a generic chaos generator map. The system performance is evaluated in terms of bit error rate, and, to obtain a performance improvement, it is also proposed to filter the out-of-band noise in the receiver. Although the conditions for chaotic synchronization have been determined, the filters insertion can also modify the chaotic nature of the signals, and there is no guarantee that the transmitted signals remain chaotic. To analyze the chaotic nature of the communication system transmitted signals, the largest Lyapunov exponent is numerically accessed as a function of the filters coefficients, the parameters of the map and the message coding function.

Greta A. Abib

Papers

On the Performance of a Digital Chaos-Based Communication System in Noisy Channels