Denoising of discrete-time chaotic signals using echo state networks

Noise reduction is a relevant topic when considering the application of chaotic signals in practical problems, such as communication systems or modeling biomedical signals. In this paper an echo state network (ESN) is employed to denoise a discrete-time chaotic signal corrupted by additive white Gaussian noise. The choice for applying ESNs in this context is motivated by their successful exploitation for separation and prediction of chaotic signals. The results show that the processing gain of ESN is higher than that of the Wiener filter, especially when the power spectral density of the chaotic signals is white.Comment: Submitted to Signal Processing - Elsevie

Chaos-Based Spectral Keying Technique for Secure Communication and Covert Data Transmission between Radar Receivers over an Open Network Channel

Application of chaotic signals in modern telecommunication facilities and radars is an actual task that can significantly extend functionality of these systems and improve their performance. In this chapter, we propose a concept of chaos-based technique for secure communication and hidden data transmission over an open network channel which is based on a novel method for spectral keying of chaotic signal generated by nonlinear dynamical system with delayed feedback. In the technique developed, the modulating information sequence controls the parameter of nonlinear element, so that it switches the chaotic modes and changes the spectral structure of the signal, transmitted to the communication channel. A noncoherent reception is used for demodulation the information message from received waveform. We start from theoretical justification of the proposed scheme, and show then the numerical simulations and imitation modeling results, as well as demonstrate experimental validation of suggested technique. Also, the communication system reliability and its covert operation efficiency under impact of AWGN in the environment with high-level interferences have been shown by means of evaluation the system anti-jamming capabilities and unauthorized access immunity

A chaotic switched-capacitor circuit for characteristic CMOS noise distributions generation

A switched-capacitor circuit is proposed for the generation of noise resembling the typical noise spectral density of MOS devices. The circuit is based on the combination of two chaotic maps, one generating 1/f noise (hopping map) and the other generating white noise (Bernoulli map). Through a programmable weighted adder stage, the contribution of each map can be controlled and, thereby, the position of the corner frequency. Behavioral models simulations were carried out to prove the correct functionality of the proposed approach.Ministerio de Economía y Competitividad TEC2016-80923-

The variation of invariant graphs in forced systems

In skew-product systems with contractive factors, all orbits asymptotically approach the graph of the so-called sync function; hence, the corresponding regularity properties primarily matter. In the literature, sync function Lipschitz continuity and differentiability have been proved to hold depending on the derivative of the base reciprocal, if not on its Lyapunov exponent. However, forcing topological features can also impact the sync function regularity. Here, we estimate the total variation of sync functions generated by one-dimensional Markov maps. A sharp condition for bounded variation is obtained depending on parameters, that involves the Markov map topological entropy. The results are illustrated with examples

Application of a MEMS-based TRNG in a chaotic stream cipher

In this work, we used a sensor-based True Random Number Generator in order to generate keys for a stream cipher based on a recently published hybrid algorithm mixing Skew Tent Map and a Linear Feedback Shift Register. The stream cipher was implemented and tested in a Field Programmable Gate Array (FPGA) and was able to generate 8-bit width data streams at a clock frequency of 134 MHz, which is fast enough for Gigabit Ethernet applications. An exhaustive cryptanalysis was completed, allowing us to conclude that the system is secure. The stream cipher was compared with other chaotic stream ciphers implemented on similar platforms in terms of area, power consumption, and throughput

Cryptographic requirements for chaotic secure communications

In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.Comment: 13 pages, 3 figure

PAPR Reduction and Data Security Improvement for OFDM Technique Using Chaos System

Orthogonal Frequency Division Multiplexing (OFDM) is the most popular multicarrier technique because it produces several advantages such as higher spectral efficiency, high transmission rate, robustness to fading channel and etc.. In this technique, the data is carrying by multiple orthogonal subcarriers. If all subcarriers are adding together with the same phase, it will result high Peak to Average Power Ratio (PAPR). Higher value of PAPR makes low power efficiency, several degradation of performance in the transmit power amplifier and increase the complexity of converters. It is important to decrease PAPR for avoid these problems. Another requirement of the modern communication system is the security of transmission data. All these issues make strong motivation for building algorithm to improve performance and security of OFDM system. In this paper, a proposed algorithm is presented to both reduce PAPR and secure the OFDM signal by generating several Aperiodic PseudoRandom Binary Sequences (APRBSs) using chaos system. The proposed algorithm is scrambling the information by APRBSs, and one sequence is chosen for transmission which has smallest PAPR value. To inform receiver which sequence had been sent, a Side Information (SI) is enclosed with the transmitted sequence. Because SI very important at receiver, convolutional code with Viterbi-Soft Decision Decoding (V-SDD) is used to protect it against channel distortion. Simulation results state the proposed algorithm produces excellent PAPR reduction performance and approximately gives the same Bit Error Rate (BER) of the conventional OFDM system over AWGN and fading channels. In addition to get better performance, the proposed algorithm is providing a good data security due to chaos system. MATLAB program is used to build the proposed OFDM system and get the simulation results

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems. Our approach follows two steps: first, we train an artificial neural network (ANN) with flicker (colored) noise to predict the value of the parameter, $\alpha$, that determines the strength of the correlation of the noise. To predict $\alpha$ the ANN input features are a set of probabilities that are extracted from the time series by using symbolic ordinal analysis. Then, we input to the trained ANN the probabilities extracted from the time series of interest, and analyze the ANN output. We find that the $\alpha$ value returned by the ANN is informative of the temporal correlations present in the time series. To distinguish between stochastic and chaotic signals, we exploit the fact that the difference between the permutation entropy (PE) of a given time series and the PE of flicker noise with the same $\alpha$ parameter is small when the time series is stochastic, but it is large when the time series is chaotic. We validate our technique by analysing synthetic and empirical time series whose nature is well established. We also demonstrate the robustness of our approach with respect to the length of the time series and to the level of noise. We expect that our algorithm, which is freely available, will be very useful to the community