Danièle Fournier-Prunaret

A Methodology for Bit Error Rate Prediction in Chaos-based Communication Systems

This paper is devoted to the derivation of an exact analytical expression of the bit error rate for chaos-based DS-CDMA systems. For the studied transmission system, we suppose that synchronization is achieved perfectly, coherent reception is considered, and an Additive White Gaussian Noise channel (AWGN) is assumed. In the first part of the paper, performance of a mono-user system with different chaotic sequences is evaluated and compared in terms of the error probability. This comparison is realized thanks to the probability density function of the bit energy of a chaotic sequence. The bit error rate can be easily derived by numerical integration. In some particular cases, for certain chaotic sequences with known probability density function of bit energy, we propose an analytical expression of the bit error. In the second part of the paper, the performance of a chaos-based DS-CDMA system is evaluated in the multi-user case. A general conclusion is that probability density function of chaos bit energy, for a given spreading factor, can give a clear idea about how to choose a “good” chaotic sequence for improving the performance of the chaos-based CDMA system.

Robust synchronization for asynchronous multi-user chaos-based DS-CDMA

In this paper we propose two systems for achieving synchronization in asynchronous multi-user chaos-based DS-CDMA. For the first system, synchronization process is realized thanks to a binary code used as an additive pilot sequence to the spreaded signal. Gold sequences are used as pilot signals for the different users to accomplish the synchronization. For the second synchronization system, the synchronization is made through a binary code used as a multiplicative pilot signal for the spreaded data sequence. These synchronization processes are evaluated under the assumption of an additive white Gaussian noise channel together with multi-user interferences. In this paper we will focus on the initial synchronization phase (code acquisition) and we assume that the system can achieve correctly the code tracking after this first synchronization phase. The code acquisition for the two systems is evaluated in terms of the probability of detection and probability of false alarm.

A DOUBLE LOGISTIC MAP

Several endomorphisms of a plane have been constructed by coupling two logistic maps. Here we study the dynamics occurring in one of them, a twisted version due to J. Dorband, which (like the other models) is rich in global bifurcations. By use of critical curves, absorbing and invariant areas are determined, inside which global bifurcations of the attracting sets (fixed points, closed invariant curves, cycles or chaotic attractors) take place. The basins of attraction of the absorbing areas are determined together with their bifurcations.

Transform domain communication systems from a multidimensional perspective, impacts on bit error rate and spectrum efficiency

Transform domain communication systems (TDCSs) is a technology that avoids frequency underutilisation. Its bit error rate (BER) performance has been well studied until now, but it is still unknown what is the maximum spectrum efficiency one can expect. Focusing on the multidimensional property of the system, the authors show the reachable BER and spectral efficiency they can obtain for any TDCS. Through this article, the authors provide guidelines to ensure that the spectral efficiency is maximised, whereas the BER is minimised. Previous contributions using TDCSs are studied with regard to their dimensionality and they show how their BER and spectral efficiency can be improved.

Accurate bit error rate calculation for asynchronous chaos-based DS-CDMA over multipath channel

An accurate approach to compute the bit error rate expression for multiuser chaosbased DS-CDMA system is presented in this paper. For more realistic communication system a slow fading multipath channel is considered. A simple RAKE receiver structure is considered. Based on the bit energy distribution, this approach compared to others computation methods existing in literature gives accurate results with low computation charge. Perfect estimation of the channel coefficients with the associated delays and chaos synchronization is assumed. The bit error rate is derived in terms of the bit energy distribution, the number of paths, the noise variance, and the number of users. Results are illustrated by theoretical calculations and numerical simulations which point out the accuracy of our approach.

NONLINEAR DYNAMICS OF BANDPASS SIGMA-DELTA MODULATION — AN INVESTIGATION BY MEANS OF THE CRITICAL LINES TOOL

Bandpass sigma-delta modulation is a technique used to convert high-frequency narrowband electronic signals from analog form to digital, or vice versa. It is a fundamentally nonlinear technique, and therefore can be analyzed only approximately by application of linear analysis. The aim of this work is to present certain results concerning the dynamical behavior of bandpass sigma-delta modulators with zero input based on application of methods of nonlinear dynamics and noninvertible map theory. We will consider the effect of certain circuit imperfections on the behavior of the system, and will also consider the effect of operating in a chaotic regime. While many of our results arise from application of standard methods of nonlinear dynamics, we will emphasize in particular those results that can be obtained by application of the critical lines tool of Mira. The paper, therefore, has two aims: To investigate the nonlinear behavior of bandpass sigma-delta modulators and to provide a demonstration of the applicability of the critical lines tool to a system of engineering importance.

Efficient and secure chaotic S-Box for wireless sensor network

Information security using chaotic dynamics is a novel topic in the wireless sensor network WSN research field. After surveying analog and digital chaotic security systems, we give a state of the art of chaotic S-Box design. The substitution tables are nonlinear maps that strengthen and enhance block crypto-systems. This paper deals with the design of new dynamic chaotic S-Boxes suitable for implementation on wireless sensor nodes. Our proposed schemes are classified into two categories: S-Box based on discrete chaotic map with floating point arithmetic cascading piecewise linear chaotic map and a three-dimensional map and S-Box based on discrete chaotic map with fixed-point arithmetic using discretized Lorenz map and logistic-tent map. The security analysis and implementation process on WSN are discussed. The proposed methods satisfy Good S-Box design criteria and exceed the performance of Advanced Encryption Standard static S-Box in some cases. The energy consumption of different proposals and existing chaotic S-Box designs are investigated via a platform simulator and a real WSN testbed equipped with TI MSP430f1611 micro-controller. The simulations and the experimental results show that our proposed S-Box design with fixed-point arithmetic Lorenz map has the lowest energy-consuming profile compared with the other studied and proposed S-Box design. Copyright

Border collision bifurcations in a two-dimensional piecewise smooth map from a simple switching circuit

In recent years, the study of chaotic and complex phenomena in electronic circuits has been widely developed due to the increasing number of applications. In these studies, associated with the use of chaotic sequences, chaos is required to be robust (not occurring only in a set of zero measure and persistent to perturbations of the system). These properties are not easy to be proved, and numerical simulations are often used. In this work, we consider a simple electronic switching circuit, proposed as chaos generator. The object of our study is to determine the ranges of the parameters at which the dynamics are chaotic, rigorously proving that chaos is robust. This is obtained showing that the model can be studied via a two-dimensional piecewise smooth map in triangular form and associated with a one-dimensional piecewise linear map. The bifurcations in the parameter space are determined analytically. These are the border collision bifurcation curves, the degenerate flip bifurcations, which only are allowed to occur to destabilize the stable cycles, and the homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in 1-piece.

On dynamic chaotic S-BOX

The substitution table or S-Box is considered as the core of the block ciphers. The good design of the S-Box can increase the cipher security and simplicity.

Analytical calculation of BER in communication systems using a piecewise linear chaotic map

The coherent reception of direct sequence-code division multiple access (DS-CDMA) is considered, when chaotic sequences are used instead of conventional pseudo-noise (PN) spreading code. A piecewise linear map (PWL) is used as chaotic spreading sequence (CSS). Additive white Gaussian noise channel (AWGN) is assumed. An analytical expression of the bit error rate in the single user case is presented.