TOPICS IN COMMUNICATIONS WITH CHAOTIC SYSTEMS

Martin Hasler, Thomas Schimming
Laboratory of Nonlinear System, School of Computer and Communication Sciences Swiss Federal Institute of Technology Lausanne (EPFL) Lausanne, Switzerland

DOI: 10.36724/2664-066X-2021-7-6-31-35

SYNCHROINFO JOURNAL. Volume 7, Number 6 (2021). P. 31-35.

Abstract

The use of chaotic systems in communications approaches the threshold for industrial applicability. We shall give here an overview over a few techniques we think are promising. However, this overview does not pretend to be complete and it contains personal views on the subject. Also, the use of chaotic system for information encryption is not discussed at all. Only a choice of methods for coding and modulation for the transmission of digital information will be presented. An overview of a number of techniques to transmit information using chaotic systems is given. The difficulties in obtaining a good performance of such systems with respect to channel noise leads to fundamental question, to which we give a possible answer. Given the generally mediocre performance of such approaches, we have identified two fundamental questions which should help us pinpoint the main problems with the existing approaches with the help of information theory and communication theory. In particular it has been confirmed both in theory and by a constructive approach leading to a controlled variant of CSK, that indeed the information generated by free running chaotic systems (as captured by the Kolmogorov-Sinai entropy) is the problem, and the solution is a suitable control that makes this information part of the payload.

Keywords:  Chaos, Communications, Noise performance, information theory, modulation, coding.

References

[1] M. Delgado-Restituto, A. Rodriguez-Vazquez. Integrated chaos generators, Proc. IEEE, vol.90, no.5, pp. 747-767, 2002.
[2] A. Baranowski, W. Schwarz. Statistical analysis and design of continuous-discrete chaos generators, Trans. IEICE, Vol. E82-A, No. 9, pp. 1762-1768, 1999.
[3] R. Rovatti, G. Mazzini, G. Setti, A. Giovanardi. Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications, Proc. IEEE, Vol. 90, No. 5, pp. 820-841, 2002.
[4] A. Dmitriev, B. Kyarginsky, A. Panas, S. Starkov. Direct chaotic communication scheme at microwave frequencies, J. of Communications Technology and Electronics, v. 46, no. 2, pp. 207-214, 2001.
[5] R. Rovatti, G. Mazzini, G. Setti. Interference bounds for DS- CDMA systems based on chaotic piecewise affine Markov maps, IEEE Trans. Circ. Syst. I, vol.47, No.6, pp.885-896, 2000.
[6] R. Rovatti, G. Mazzini, G. Setti. Enhanced rake receivers for chaos-based DS-CDMA, IEEE Trans. Circ. Syst. I, vol.48, No. 7, pp. 818-829, 2001.
[7] H. Dedieu, M.P. Kennedy, M. Hasler. Chaos shift keying: modulation of a chaotic carrier using self-synchronizing Chua’s circuits, IEEE Trans. Circ. Syst. II, Vol.40, pp. 634- 642, 1993.
[8] Yu.L. Bel’skii, A.S. Dmitriev. Information transmission using deterministic chaos (in Russian), Radiotechnika i Elektronika (Russian Academy of Science), Vol.38, pp. 1310-1315, 1993.
[9] C.W. Wu, L.O. Chua. Transmission of digital signals  by chaotic synchronization, Int. J. Bif. Chaos, Vol.3, no.6, pp. 1619-1627, 1993.
[10] G. Kolumban, K. Vizvari, A. Abel, W. Schwarz. Differential chaos shift-keying: a robust coding for chaos communication, Proc. NDES 1996, Seville, Spain, pp. 87-92, 1996.
[11] M. Hasler, T. Schimming. Optimal and suboptimal chaos receivers, Proc. IEEE, vol.90, no.5, pp.733-746, 2002.
[12] A. Abel, W. Schwarz. Chaos communications – principles, schemes and system analysis, Proc. IEEE, vol.90, no.5, pp. 791-710, 2002.
[13] G. Kolumban, M.P. Kennedy, Z. Jako, G. Kis. Chaotic communications with correlation receivers: theory and performance limits, Proc. IEEE, vol.90, no.5, pp. 711-732, 2002.
[14] K. Krol, L. Azzinnari, E. Korpela, A. Mozsari, M. Talonen, V. Porra. An experimental FM-DCSK chaos radio system, Proc. ECCTD-2001, Espoo, Finland, vol.3, pp. 17-20, 2001.
[15] M.P. Kennedy, G. Kolumban, G. Kis, Z. Jako. Performance evaluation of FM-DCSK modulation in multipath environments, IEEE Transaction on Circuits and Systems-1, Vol. 47, pp. 1 772-1711, 2000.
[16] T. Schimming. Chaos based modulations from  an information theory perspective, Proc. ISCAS 2001, Sidney, Australia, Vol.3, pp. 309-312. 2001.
[17] T. Cover, J. Thomas. Elements of information theory, Wiley & Sons, New York, 1991.
[18] Hao Bai-lin. Applied symbolic dynamics and chaos, World- Scientific, Singapore, 1998.
[19] S. Hayes, C. Grebogy, E. Ott. Communicating with chaos, Phys.Rev.Lett., Vol.70, pp. 3031-3034, 1993.
[20] J. Schweizer, M.P. Kennedy. Predictive Poincaré control modulation: a new method for modulating digital information onto a chaotic carrier signal, Irish DSP and Control Colloquium, Dublin, Ireland, pp.125-132. 1994.
[21] S. Kozic, K. Oshima, T. Schimming. Minimum Distance Properties of coded modulations based on iterated chaotic maps, Proc. ECCTD 2002, Krakov, Poland, 2003.
[22] J.G. Proakis, Digital Communications, McGraw-Hill, 1995.