Discrete Chaotic Signals Research Articles

СТАТИСТИЧЕСКИЕ ХАРАКТЕРИСТИКИ СИСТЕМЫ ОТНОСИТЕЛЬНОЙ ПЕРЕДАЧИ ИНФОРМАЦИИ НА ОСНОВЕ ХАОТИЧЕСКИХ ИМПУЛЬСОВ В КАНАЛЕ С ГАУССОВСКИМ ШУМОМ

The purpose of this paper is to analyze the statistical characteristics of a differentially coherent communication scheme based on the use of chaotic pulses in the presence and absence of thermal noise for various distributions of chaotic signal instantaneous values. To achieve this goal, a numerical simulation for the performance of direct chaotic differentially coherent communication scheme is carried out in the work by a computer simulation. A numerical simulation was carried out, confirming the previously obtained analytical bit error probability estimates vs energy per bit to gaussian noise power spectral density ratio. The minimum energy per bit to gaussian noise power spectral density ratio values, which provide the given error probabilities, are obtained. It is shown that the proposed communication system works effectively at high values of processing gain(the behavior of the communication system was studied for various values of processing gain), and in the case of high values of processing gain, the results obtained do not depend on the choice of a specific discrete chaotic signal distribution.

Информационные технологии на основе шумоподобных сигналов: II. Cтатистические и фрактальные свойства хаотических алгоритмов

On the basis of nonlinear systems with dynamic chaos, discrete chaotic signals with high information capacity have been developed and studied. The influence of the main parameters of a generating chaotic algorithm with delay on the statistical, correlation, structural and fractal characteristics of non-periodic pseudo-random integer and binary sequences generated by the algorithm is analyzed by numerical methods. It is shown that non-periodic pseudo-random sequences (PRS) generated by a chaotic algorithm with delay, for all values of the main parameters, have good statistical, correlation, structural and fractal characteristics, close to random sequences of independent trials. It is shown that these characteristics are provided on a long PRS cycle in a multidimensional phase space for all the main parameters of the chaotic algorithm and an arbitrary choice of initial conditions. Such binary PRSs can be quite effectively used in telecommunication systems using streaming coding of large blocks of information messages from the point of view of secrecy, noise immunity and cryptographic stability of the communication channel.

Speech compression and encryption based on discrete wavelet transform and chaotic signals

To increase transfer and storage efficiencies of the information, data compression has emerged as a significant issue in the communication environments. This paper introduces compression and encryption of speech signals based on Discrete Wavelet Transform (DWT) and Chaotic signals. DWT sparsens and codes the speech signal to the wavelet coefficients. The less impactful coefficients are eliminated to reduce the amount of data. After that, a new coding process which utilizes the chaotic signals is proposed to encode, in encrypted form, the residual coefficients. A High strength to the encryption process is realized by using four linked Henon Chaotic Maps (HCM) in the proposed scheme. Multi HCM guarantees larger than 10240 of key space to the encryption process. The proposed system obtains up to −41.449 dB of spectral segmental signal-to-noise ratio, which measures and proves the strength of encryption. Also, at 10% compression ratio, signal-to-noise ratio of 11.549 dB and perceptual evaluation speech quality of 3.02945 demonstrate that the proposed system has high quality and intelligibility of the reconstructed speech.

전압 제어형 카오스회로의 온도특성 해석

This paper presents a temperature analysis of the chaotic behavior in the voltage controlled CMOS chaotic circuit. The circuit is based on a simple nonlinear function block which is needed for chaotic signal generation. It consists of a NFB (nonlinear function block), a level shifter and non-overlapping two-phase clock for sample and hold. By SPICE simulation, chaotic dynamics such as frequency spectra and bifurcations according to the temperature variations were analyzed. And, it was showed that the circuit can generate discrete chaotic signals within control voltage in the range from 1.2 V to 2.3 V in a specific temperature condition of .

Effect of Temperature on a Two-Phase Clock-Driven Discrete-Time Chaotic Circuit

The effects of temperature on a two-phase clock-driven discrete-time chaotic circuit are presented. The circuit for temperature analysis consists of two switches for sample and hold, a source follower, and a nonlinear function for nonlinearity in the feedback. The chaotic dynamics of this circuit, such as time series, state transitions, frequency spectra bifurcation diagrams and Lyapunov exponents are analyzed as functions of the temperature. It is confirmed that the dynamics of the chaotic circuit have a temperature dependence. Further, we find that the circuit can generate discrete chaotic signals only within specific temperature regions.

Chaotic dynamics of a three-phase clock-driven oscillator with dual voltage controllability

In this work, we study a novel dual-voltage-controlled chaotic oscillator by using a three-phase clock. The chaotic oscillator is based on two nonlinear functions, which are needed for chaotic signal generation. The proposed chaotic circuit consists of three non-overlapping clock-driven MOS (metal oxide semiconductor) switches for S/H (sample and hold), a level shifter, and two nonlinear functions for nonlinearity in the feedback. After nonlinear functions for chaotic signal generation had been optimized, the proposed circuit was simulated with SPICE (Simulation Program with Integrated Circuit Emphasis) program using a 0.6 µm CMOS (complementary metal oxide semiconductor) process parameter. For various control voltages, its chaotic dynamics, such as time waveform, bifurcation diagram and state transition diagram were analyzed. We confirmed that the circuit could generate discrete chaotic signals in specific control voltages. This circuit is expected to be utilized for various chaos applications.

Multiplexing of discrete chaotic signals in presence of noise

Multiplexing of discrete chaotic signals in presence of noise is investigated. The existing methods are based on chaotic synchronization, which is susceptible to noise, precision limitations, and requires more iterates. Furthermore, most of these methods fail for multiplexing more than two discrete chaotic signals. We propose novel methods to multiplex multiple discrete chaotic signals based on the principle of symbolic sequence invariance in presence of noise and finite precision implementation of finding the initial condition of an arbitrarily long symbolic sequence of a chaotic map. Our methods work for single precision and as less as 35 iterates. For two signals, our method is robust up to 50% noise level.

Complex chaotic discrete signals in telecommunications, radar, and navigation systems

Discrete chaotic signals with a high information capacity are developed and studied on the basis of nonlinear chaotic dynamic systems. The structural and fractal complexity of pseudorandom integer and binary sequences is analyzed. A model digital spread-spectrum radio channel is used to show experimentally that the chaotic algorithms developed can be applied efficiently in various radio facilities, such as telecommunications, radar, and navigation systems. A technique is developed for forming a reproducible irregular fractal structure involved in frequency-independent fractal antennas with a given fractal dimension. An integer chaotic algorithm with retardation is employed to generate a pseudorandom sequence.

Implementation of a new chaotic encryption system and synchronization

Abstract A new kind of secure communication system which combines the chaotic encryption means with the conventional encryption method is discussed. With the analysis results and the experiment data, the anti-attack ability of this communication system is significantly improved compared to that of the either method. At the same time, a new method of chaotic synchronization is proposed. With a small mixed discrete chaotic signal, it is quickly to synchronize the communication and a good security performance is ensured.

The Hausdorff dimension of very weak self-similar fractals described by the Haar wavelet system

We observe that most signals can be described as Riesz products in the Haar wavelet system and a wide class of these products are fractals with a very weak self-similarity. For this class we show the relation of the Hausdorff dimension and the entropy of the corresponding process. Moreover we give a formula for experimental estimates of the entropy of discrete chaotic signals.