Co-existence of chaos-based and conventional digital communication systems

Author name used in this publication: Francis C. M. LauAuthor name used in this publication: Chi K. TseRefereed conference paper2002-2003 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe

Efficient error correcting scheme for chaos shift keying signals

An effective error-correction scheme based on normalized correlation for a non coherent chaos communication system with no redundancy bits is proposed in this paper. A modified logistic map is used in the proposed scheme for generating two sequences, one for every data bit value, in a manner that the initial value of the next chaotic sequence is set by the second value of the present chaotic sequence of the similar symbol. This arrangement, thus, has the creation of successive chaotic sequences with identical chaotic dynamics for error correction purpose. The detection symbol is performed prior to correction, on the basis of the suboptimal receiver which anchors on the computation of the shortest distance existing between the received sequence and the modified logistic map’s chaotic trajectory. The results of the simulation reveal noticeable Eb/No improvement by the proposed scheme over the prior to the error- correcting scheme with the improvement increasing whenever there is increase in the number of sequence N. Prior to the error-correcting scheme when N=8, a gain of 1.3 dB is accomplished in Eb/No at 10-3 bit error probability. On the basis of normalized correlation, the most efficient point in our proposed error correction scheme is the absence of any redundant bits needed with minimum delay procedure, in contrast to earlier method that was based on suboptimal method detection and correction. Such performance would render the scheme good candidate for applications requiring high rates of data transmission

Multi user chaotic communication systems sing orthogonal chaotic vectors

Due to quasi orthogonal nature of chaotic spreading sequences, the co-channel interference will be introduced and increases with the increase in number of users and limits the number of simultaneous users transmitting information. In this dissertation the application of orthogonal chaotic vector (OCV) for spreading information bits is presented. The bit error rate of the multi user chaotic communication system is analysed through simulation and analytical expressions. Two main types of communication scenarios are considered, multi user chaotic communication system with coherent receiver and training assisted non coherent multi user chaotic communication system with adaptive receiver. The first case deals with ideal scenario where it is assumed that exact replica of chaotic vector used to spread data is available at the receiver and the information is extracted without synchronisation error. Thus lacks practical realisation but, the results obtained will provide a lower bound for comparison with other practical counter parts. The second scenario deals with more practical approach where a reference chaotic sequence is also transmitted by modulating with training bits so that the chaotic vector required for correlation can be recovered at the receiver

Chaos synchronization and its application to secure communication

Chaos theory is well known as one of three revolutions in physical sciences in 20th-century, as one physicist called it: Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurable process; and chaos eliminates the Laplacian fantasy of deterministic predictability". Specially, when chaos synchronization was found in 1991, chaos theory becomes more and more attractive. Chaos has been widely applied to many scientific disciplines: mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics. One of most important engineering applications is secure communication because of the properties of random behaviours and sensitivity to initial conditions of chaos systems. Noise-like dynamical behaviours can be used to mask the original information in symmetric cryptography. Sensitivity to initial conditions and unpredictability make chaotic systems very suitable to construct one-way function in public-key cryptography. In chaos-based secure communication schemes, information signals are masked or modulated (encrypted) by chaotic signals at the transmitter and the resulting encrypted signals are sent to the corresponding receiver across a public channel (unsafe channel). Perfect chaos synchronization is usually expected to recover the original information signals. In other words, the recovery of the information signals requires the receiver's own copy of the chaotic signals which are synchronized with the transmitter ones. Thus, chaos synchronization is the key technique throughout this whole process. Due to the difficulties of generating and synchronizing chaotic systems and the limit of digital computer precision, there exist many challenges in chaos-based secure communication. In this thesis, we try to solve chaos generation and chaos synchronization problems. Starting from designing chaotic and hyperchaotic system by first-order delay differential equation, we present a family of novel cell attractors with multiple positive Lyapunov exponents. Compared with previously reported hyperchaos systems with complex mathematic structure (more than 3 dimensions), our system is relatively simple while its dynamical behaviours are very complicated. We present a systemic parameter control method to adjust the number of positive Lyapunov exponents, which is an index of chaos degree. Furthermore, we develop a delay feedback controller and apply it to Chen system to generate multi-scroll attractors. It can be generalized to Chua system, Lorenz system, Jerk equation, etc. Since chaos synchronization is the critical technique in chaos-based secure communication, we present corresponding impulsive synchronization criteria to guarantee that the receiver can generate the same chaotic signals at the receiver when time delay and uncertainty emerge in the transmission process. Aiming at the weakness of general impulsive synchronization scheme, i.e., there always exists an upper boundary to limit impulsive intervals during the synchronization process, we design a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS). IISS can not only be flexibly applied to the scenario where the control window is restricted but also improve the security of chaos-based secure communication via reducing the control window width and decreasing the redundancy of synchronization signals. Finally, we propose chaos-based public-key cryptography algorithms which can be used to encrypt synchronization signals and guarantee their security across the public channel

Potential of chaos communication over noisy channels - Channel coding using chaotic piecewise linear maps

The paper gives an information theoretic analysis of the potential of chaos in digital communication schemes, underlining that there is no fundamental principle that speaks against the use of chaotic systems in digital communications. The channel model considered throughout the paper is that of additive white Gaussian noise (AWGN). In particular, an example using the dyadic shift (Bernoulli shift) map is presented to illustrate the fact that the use chaotic piecewise linear maps has no systematic negative effect for digital communications applications