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This chapter provides a brief overview of some of the digital communications techniques that have been proposed recently employing nonlinear dynamics, along with a comparison to traditional approaches. Both wireless modulation techniques as well as optical communications approaches are be presented.

We review a new approach to communication with chaotic signals based upon chaotic signals in the form of pulse trains where intervals between the pulses are determined by chaotic dynamics of a pulse nary information is modulated onto this carrier by the pulse position modulation method, such that each pulse is either left unchanged or delayed by a certain time, depending on whether 0 or 1 is transmitted. By synchronizing the receiver to the chaotic-pulse train we can anticipate the timing of pulses corresponding to 0 and 1 and thus can decode the transmitted information. Based on the results of theoretical and experimental studies we discuss the basic design principles for the chaotic-pulse generator, its synchronization, and the performance of the chaotic-pulse communication scheme in the presence of channel noise and filtering.

We describe two different approaches to employ chaotic signals in spread-spectrum (SS) communication systems with phase and frequency modulation. In the first one a chaotic signal is used as a carrier. We demonstrate that using a feedback loop controller, the local chaotic oscillator in the receiver can be synchronized to the transmitter. The information can be transmitted using phase or frequency modulation of the chaotic carrier signal. In the second system the chaotic signal is used for frequency modulation of a voltage controlled oscillator (VCO) to provide a SS signal similar to frequency hopping systems. We show that in a certain parameter range the receiver VCO can be synchronized to the transmitter VCO using a relatively simple phase lock loop (PLL) circuit. The same PLL is used for synchronization of the chaotic oscillators. The information signal can be transmitted using a binary phase shift key (BPSK) or frequency shift key (BFSK) modulation of the frequency modulated carrier signal. Using an experimental circuit operating at radio frequency band and a computer modeling we study the bit error rate (BER) performance in a noisy channel as well as multiuser capability of the system.

Pseudo-chaotic time hopping (PCTH) is a recently proposed encoding/modulation scheme for UWB (ultra-wide band) impulse radio. PCTH exploits concepts from symbolic dynamics to generate aperiodic spreading sequences, resulting in a noiselike spectrum. In this chapter we present the signal characteristics of single-user PCTH as well as a suitable multiple access technique. In particular, we provide analytical expressions for the BER (bit-error-rate) performance as a function of the number of users and validate it by simulation.

This chapter presents a tutorial and overview of the interplay among nonlinear dynamical system theory, ergodic theory, and the design and analysis of spreading sequences for CDMA communication systems. We first address some motivational factors in information theory, communication theory, and communication systems to chaotic communication systems. Then we consider some basic issues in CDMA communication system. Next we summarize some properties of nonlinear dynamical system and ergodic theories needed for this study. Some history and details on the design and analysis of optimum chaotic asynchronous and chip-synchronous spreading sequences for CDMA systems are given. These optimum spreading sequences allow about 15% more users than random white sequences/Gold codes in an asynchronous system and 73% more users in a chip-synchronous system. Comparisons of performance of these system under ideal and practical conditions are also made. Finally, some brief conclusions are given.

The turbo decoding algorithm is a high-dimensional dynamical system parameterized by a large number of parameters (for a practical realization the turbo decoding algorithm has more than 10 variables and is parameterized by more than 10 parameters). In this chapter we treat the turbo decoding algorithm as a dynamical system parameterized by a single parameter that closely approximates the signal-to-noise ratio (SNR). A whole range of phenomena known to occur in nonlinear systems, such as the existence of multiple fixed points, oscillatory behavior, bifurcations, chaos, and transient chaos are found in the turbo decoding algorithm. We develop a simple technique to control transient chaos in the turbo decoding algorithm and improve the performance of the standard turbo codes.

During the last decade a new approach for secure communication, based on chaotic dynamics attracted the attention of the scientific community. In this chapter we give an overview and describe the research that was done at the Institute for Nonlinear Science (INLS) on this topic. We begin this chapter with a brief introduction to chaos-based encryption schemes. We then describe a new method for public key encryption that we have developed which is based on distributed chaotic dynamics. Next, we lay out a quantitative cryptanalysis approach for symmetric key encryption schemes that are based on active/passive decomposition of chaotic dynamics. We end this chapter with a summary and suggestions for future research.

The ‘industry-strength’ data models are complex to use and tend to obscure the fundamental issues. Going back to the original proposal of Chen for Entities and Relationships, I describe here a reduced data model with Objects and Relations. It is mathematically well founded in the category of relations and has been implemented to demonstrate that it is viable. An example how this is used to structure data and load data is shown.

The most important numerical tools needed in the analysis of chaotic systems performing chaos synchronization and chaotic communications are discussed in this chapter. Basic concepts, theoretical framework, and computer algorithms are reviewed. The subjects covered include the concepts and numerical simulations of stochastic nonlinear systems, the complexity of a chaotic attractor measured by Lyapunov exponents and correlation dimension, the robustness of synchronization measured by the transverse Lyapunov exponents in parameter-matched systems and parameter-mismatched systems, the quality of synchronization measured by the correlation coefficient and the synchronization error, and the treatment of channel noise for quantifying the performance of a chaotic communication system. For a dynamical system described by stochastic differential equations, the integral of a stochastic term is very different from that of a deterministic term. The difference and connection between two different stochastic integrals in the Ito and Stratonovich senses, respectively, are discussed. Numerical algorithms for the simulation of stochastic differential equations are developed. Two quantitative measures, namely, the Lyapunov exponents and the correlation dimension, for a chaotic attractor are discussed. Numerical methods for calculating these parameters are outlined. The robustness of synchronization is measured by the transverse Lyapunov exponents. Because perfect parameter matching between a transmitter and a receiver is generally not possible in a real system, a new concept of measuring the robustness of synchronization by comparing the unperturbed and perturbed receiver attractors is introduced for a system with parameter mismatch. For the examination of the quality of synchronization, the correlation coefficient and the synchronization error obtained by comparing the transmitter and the receiver outputs are used. The performance of a communication system is commonly measured by the bit-error rate as a function of signal-to-noise ratio. In addition to the noise in the transmitter and the receiver, the noise of the communication channel has to be considered in evaluating the bit-error rate and signal-to-noise ratio of the system. An approach to integrating the linear and nonlinear effects of the channel noise into the system consistently is addressed. Optically injected single-mode semiconductor lasers are used as examples to demonstrate the use of these numerical tools.

The objective of this chapter is to provide a complete picture of the nonlinear dynamics and chaos synchronization of single-mode semiconductor lasers for chaotic optical communications. Basic concepts and theoretical framework are reviewed. Experimental results are presented to demonstrate the fundamental concepts. Numerical computations are employed for mapping the dynamical states and for illustrating certain detailed characteristics of the chaotic states. Three different semiconductor laser systems, namely, the optical injection system, the optical feedback system, and the optoelectronic feedback system, that are of most interest for high-bit-rate chaotic optical communications are considered. The optical injection system is a nonautonomous system that follows a period-doubling route to chaos. The optical feedback system is a phase-sensitive delayed-feedback autonomous system for which all three known routes, namely, period-doubling, quasiperiodicity, and intermittency, to chaos can be found. The optical feedback system is a phase-insensitive delayed-feedback autonomous system that follows a quasiperiodicity route to chaotic pulsing. Identical synchronization in unidirectionally coupled configurations is the focus of discussions for chaotic communications. For optical injection and optical feedback systems, the frequency, phase, and amplitude of the optical fields of both transmitter and receiver lasers are all locked in synchronism when complete synchronization is accomplished. For the optoelectronic feedback system, chaos synchronization involves neither the locking of the optical frequency nor the synchronization of the optical phase. For both optical feedback and optoelectronic feedback systems, where the transmitter is configured with a delayed feedback loop, anticipated and retarded synchronization can be observed as the difference between the feedback delay time and the propagation time from the transmitter laser to the receiver laser is varied. For a synchronized chaotic communication system, the message encoding process can have a significant impact on the quality of synchronization and thus on the message recoverability at the receiver end. It is shown that high-quality synchronization can be maintained when a proper encoding scheme that maintains the symmetry between the transmitter and the receiver is employed.