Thomas Schimming

Chaos communication over noisy channels

The problem of transmitting digital information using chaotic signals over a channel with Gaussian white noise perturbation is introduced rigorously. It is shown that discrete time base-band chaotic communication systems with discrete time Gaussian white noise in the channel are sufficiently general in this context. The optimal receiver is given explicitly in terms of conditional probabilities. For the example of chaos shift keying using iterations of the tent map, the optimal classifier is constructed explicitly. Finally, it is shown how previously published methods, in particular those based on chaos synchronization, fit into this framework.

Symbolic dynamics for processing chaotic signal. II. Communication and coding

For pt. I see ibid., vol. 48, no. 11, p. 1269-82 (2001). The idea of using chaotic signals in different layers of communication systems has attracted the attention of researchers as well as engineers and many encryption, coding, and modulation schemes have been proposed in recent years. One promising application is to employ chaotic codes in broadband communication with the intention of achieving a better immunity to multipath degradation and self-interference, exploiting the nonperiodicity of chaotic signals. The main drawback is that an optimum, coherent detection cannot be implemented since a synchronized reference signal on the receiver side has been, so far, only realizable for a finite number of code-words. This paper provides the analysis and results (theoretic and numerical) regarding design and optimization of chaos-based communication schemes, in particular: 1) performance limits for optimum coding and decoding schemes are derived, that are based on an infinite number of finite-length chaotic sequences that are generated by a special class of chaotic systems; 2) identification of fundamental differences between a finite set of conventional block codes and chaotic codes; and 3) development of optimization rules for chaotic codes.

Optimal detection of differential chaos shift keying

Recent advances in the development of communication schemes based on chaos suggest that differential chaos shift keying (DCSK) is one of the most promising candidates for a feasible implementation. Traditionally, the demodulation-decoding of DCSK has been achieved by means of a noncoherent approach based on a correlation detector This approach in general works fur any differential noise shift keying out of which DCSK is a subclass, i.e., it does not exploit the chaotic dynamics involved. In this paper it is shown that the simple correlation detector can be augmented by information based on the chaotic dynamics to improve the performance, yielding a statistically optimal detection. Introducing a rigorous probabilistic framework, the optimal receiver for additive white Gaussian noise is derived, and it is shown that it decomposes into a part based an correlation and a part based on the chaotic dynamics.

Symbolic dynamics for processing chaotic signals. I. Noise reduction of chaotic sequences

Chaotic signals attracted the attention among researchers because of their rich dynamics and their random-like behavior. What has been missing so far is an appropriate characterization of chaotic systems from a signal-processing point of view. This paper demonstrates that the framework of symbolic dynamics gives the possibility to partition the infinite number of finite-length trajectories of the piecewise-linear chaotic system into a countable number of trajectory-sets with common statistical properties. It turns out that this partitioning allows to derive noise-reduction schemes directly from the maximum-likelihood criteria. For the two proposed noise-reduction methods, the upper performance limits are given in an analytical form and the results are verified by applying the schemes to different types of one dimensional piecewise-linear Markov maps.

Maximum likelihood approaches for noncoherent communications with chaotic carriers

This paper deals with two problems. The first one is the noise decontamination of chaotic carriers using a maximum likelihood approach, the second is the design of communications schemes with chaotic carriers. After presenting improvements of the noise decontamination algorithms, we apply them in communication schemes. Experimental evidences show competitive capabilities of the proposed schemes with respect to the existing chaos-based modulation-demodulation techniques. In our approach we assume that the dynamics of the carriers are known in advance.

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 of chaotic piecewise linear maps has no systematic negative effect for digital communications applications.

Controlled One- and Multidimensional Modulations Using Chaotic Maps

Recently, several approaches for communications using chaos have been presented, often showing less than acceptable performance. In this paper, a short introduction to the topic is given, and it is shown that such methods can be efficient-if the information production related to the chaos in the transmitter is controlled and used for the payload of the communication. The influence of minimum distance aspects, a previously ignored key point, to the design of appropriate controlled schemes are studied. In terms of applicable theory, a link between schemes based on one-dimensional and multidimensional chaotic systems (as presented in this paper) and convolutional codes will be established. In order to support our argument, we give simulation results for some a priori examples and results of search procedure for more powerful modulations

Coded modulation based on higher dimensional chaotic maps

In this paper, we examine coded modulations based on iterations of higher dimensional piece-wise linear maps (PWLM). Particularly, we study a generalization of the Bernoulli map in higher dimensions and its application to communications. In the proposed scheme, we show that the transmitted information corresponds to the dynamics of the chaotic systems controlled by small perturbations. Minimum distance properties of the proposed class of codes are analyzed and it is pointed out that they perform much better compared to 1D systems.

Coded modulations based on controlled 1-D and 2-D piecewise linear chaotic maps

In this paper, the authors examine the use of chaotic systems based on the iteration of 1D and 2D piecewise linear chaotic maps in a coded modulation scheme. In the proposed scheme, the transmitted information is imposed on the dynamics of the chaotic systems by a small perturbation control method. By means of this control method, the system is driven in such a way that the symbolic sequence associated with the produced signal corresponds to the payload information, up to a possible coding delay. We investigate such systems and, in particular, their relation with trellis coded modulations. We show particular examples with good performance for real and complex valued Gaussian channels.

Optimal receiver for ergodic chaos shift keying

The recent proposal of ergodic chaos shift keying (ECSK) has been able to provide a viable compromise between chaos shift keying (CSK) schemes - using optimal detectors on the upper (performance) boundary - and schemes using synchronization - on the lower (performance) boundary. This compromise is interesting for applications due to the computational complexity of the optimal method, which in practice prohibits its implementation. Previously, the design of an ECSK scheme had been based on a simplistic criterion, i.e. the maximization of the decision variables mean. This paper provides a systematic approach to optimizing the receiver of an amplitude modulated implementation of ECSK (AM-ECSK) based on the assumption of a Gaussian decision variable.