Abstract
Chaotic communication can be regarded as a paradigm shift. The intensive use of the inherent complexity of chaotic oscillators allows the deployment of highly efficient codification and modulation schemes in the chaotic evolution, while the simplicity of chaos-generating devices permits simple and cost-effective hardware implementation. This paper outlines the current trends of chaos-based communication and points the challenging topics that require further attention towards the realization of widespread chaos communication.
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References
Aburakawa, Y., Otsu, T.: Dense wavelength division multiplexed optical wireless link towards terabit transmission. In: Microwave Photonics, 2003. MWP 2003 Proceedings. International Topical Meeting on, pp. 135–138, DOI 10.1109/MWP.2003.1422846 (2003)
Alligood, K.T., Sauer, T.D., Yorke, J.A.: (1997) Chaos: An Introduction to Dynamical Systems. Textbooks In Mathematical Sciences, Springer, New York (2003)
Argyris, A., Grivas, E., Hamacher, M., Bogris, A., Syvridis, D.: Chaos-on-a-chip secures data transmission in optical fiber links. Opt. Express 18(5), 5188–5198, DOI 10.1364/OE.18.005188 (2010)
Argyris, A., Syvridis, D., Larger, L., Annovazzi-Lodi, V., Colet, P., Fischer, I., Garcia-Ojalvo, J., Mirasso, C., Pesquera, L., Shore, K.: Chaos-based communications at high bit rates using commercial fibre-optic links. Nature 438(7066), 343–346, DOI 10.1038/nature042752 (2005)
Arroyo, D., Alvarez, G., Fernandez, V.: A basic framework for the cryptanalysis of digital chaos-based cryptography. In: Systems, Signals and Devices, 2009. SSD ’09. 6th International Multi-Conference on, pp. 1 –6, DOI 10.1109/SSD.2009.4956652 (2009)
Avila, J.F.M., Leite, J.R.R.: Time delays in the synchronization of chaotic coupled lasers with feedback. Opt. Express 17(24), 21,442–21,451, DOI 10.1364/OE.17.021442 (2009)
Baptista, M.S., Macau, E.E., Grebogi, C., Lai, Y.C., Rosa, E.: Integrated chaotic communication scheme. Phys. Rev. E 62(4), 4835–4845, DOI 10. 1103/PhysRevE.62.4835 (2000)
Bollt, E., Lai, Y.C., Grebogi, C.: Coding, channel capacity, and noise resistance in communicating with chaos. Phys. Rev. Lett. 79(19), 3787–3790, DOI 10.1103/PhysRevLett.79.3787 (1997)
Carroll, M., Williams, C.: Symbolic dynamics method for chaotic communications. In: MILCOM 2002. Proceedings, vol. 1, pp. 232–236, DOI 10.1109/MILCOM.2002.1180445 (2002)
Carroll, T.L., Pecora, L.M.: Using multiple attractor chaotic systems for communication. Chaos: An Interdisciplinary Journal of Nonlinear Science 9(2), 445–451, DOI 10.1063/1.166425 (1999)
Cawley, R., Hsu, G.H.: Local-geometric-projection method for noise reduction in chaotic maps and flows. Phys. Rev. A 46(6), 3057–3082, DOI 10.1103/PhysRevA.46.3057 (1992)
Chen, H., Feng, J., Fang, Y.: Blind extraction of chaotic signals by using the fast independent component analysis algorithm. Chin. Phys. Lett. 25, 405–408 (2008)
Cuomo, K.M., Oppenheim, A.V.: Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 71(1), 65–68, DOI 10.1103/PhysRevLett.71.65 (1993)
Dedieu, H., Kisel, A.: Communications with chaotic time series: probabilistic methods for noise reduction. Int. J. Circ. Theor. Appl. 27(6), 577–587 (1999)
Djurovic, I., Rubezic, V.: Chaos detection in chaotic systems with large number of components in spectral domain. Signal Process. 88(9), 2357–2362, DOI 10.1016/j.sigpro.2008.03.003 (2008)
Eisencraft, M., do Amaral, M.A.: Estimation of nonuniform invariant density chaotic signals with applications in communications. In: Second IFAC meeting related to analysis and control of chaotic systems, London, England, pp. 1–6 (2009)
Eisencraft, M., Baccalá, L.A.: The Cramer-Rao bound for initial conditions estimation of chaotic orbits. Chaos, Solitons Fractals 38(1), 132–139, DOI 10.1016/j.chaos.2006.10.067 (2008)
Eisencraft, M., Gerken, M.: Comunicação utilizando sinais caóticos: influência de ruído e limitação em banda. In: Anais do XVIII Simpósio Brasileiro de Telecomunicações, Gramado, Brasil, pp. 1–6, (in Portuguese) (2001)
Eisencraft, M., Kato, D.M.: Spectral properties of chaotic signals with applications in communications. Nonlinear Anal. Theor. Meth. Appl. 71(12), e2592–e2599, DOI 10.1016/j.na.2009.05.071 (2009)
Eisencraft, M., do Amaral, M.A., Lima, C.A.M.: Estimation of chaotic signals with applications in communications. In: Proc. 15th IFAC Symposium on System Identification, Saint-Malo, France, pp. 1–6 (2009)
Eisencraft, M., Fanganiello, R., Baccala, L.: Synchronization of discrete-time chaotic systems in bandlimited channels. Math. Probl. Eng., DOI 10.1155/2009/207971 (2009)
Eisencraft, M., Kato, D., Monteiro, L.: Spectral properties of chaotic signals generated by the skew tent map. Signal Process. 90(1), 385–390, DOI 10.1016/j.sigpro.2009.06.018 (2010)
Endo, T., Chua, L.: Chaos from phase-locked loops. IEEE Trans. Circ. Syst. 35(8), 987–1003, DOI 10.1109/31.1845 (1988)
Erneux, T.: Applied delay differential equations, 1st edn. Springer (2009)
Faleiros, A.C., Perrella, W.J., Rabello, T.N., Santos, A.S., Soma, N.Y.: Chaotic signal generation and transmission. In: [77] (2005)
Grassberger, P., Procaccia, I.: Measuring the strangeness of strange attractors. Phys. D Nonlinear Phenom. 9(1-2), 189–208, DOI 10.1016/ 0167-2789(83)90298-1 (1983)
Grebogi, C., Lai, Y.C.: Controlling chaotic dynamical systems. Syst. Contr. Lett. 31(5), 307–312, DOI 10.1016/S0167-6911(97)00046-7 (1997)
Grzybowski, J.M.V., Rafikov, M.: Sincronização do sistema caótico unificado via controle ótimo linear feedback e aplicação em comunicação segura. Tendências em Matemática Aplicada e Computacional 9(1), 105–114, (in Portuguese) (2008)
Grzybowski, J.M.V., Macau, E.E.N., Yoneyama, T.: Isochronal synchronization of time delay and delay-coupled chaotic systems. Journal of Physics A: Mathematical and Theoretical 44 (2011) 175103
Gu, K., Kharitonov, V., Chen, J.: Stability of time-delay systems, 1st edn. Birkhäuser Boston (2003)
Harb, B.A., Harb, A.M.: Chaos and bifurcation in a third-order phase locked loop. Chaos, Solitons Fractals 19(3), 667–672, DOI 10.1016/ S0960-0779(03)00197-8 (2004)
Hasler, M., Schimming, T.: Optimal and suboptimal chaos receivers. Proc. IEEE 90(5), 733–746, DOI 10.1109/JPROC.2002.1015004 (2002)
Hayes, S., Grebogi, C., Ott, E.: Communicating with chaos. Phys. Rev. Lett. 70(20), 3031–3034 (1993)
Hayes, S., Grebogi, C., Ott, E., Mark, A.: Experimental control of chaos for communication. Phys. Rev. Lett. 73(13), 1781–1784 (1994)
Hénon, M.: A two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50(1), 69–77 (1976)
Itoh, M., Chua, L.: Multiplexing techniques via chaos. In: Circuits and Systems, 1997. ISCAS ’97., Proceedings of 1997 IEEE International Symposium on, vol. 2, pp. 905–908, DOI 10.1109/ISCAS.1997.621860 (1997)
Kennedy, M., Setti, G., Rovatti, R. (eds.): Chaotic Electronics in Telecommunications. CRC Press, Boca Raton, FL, USA (2000)
Kennedy, M.P., Kolumbán, G.: Digital communications using chaos. Signal Process. 80(7), 1307–1320, DOI 10.1016/S0165-1684(00)00038-4 (2000)
Kisel, A., Dedieu, H., Schimming, T.: Maximum likelihood approaches for noncoherent communications with chaotic carriers. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 48(5), 533–542, DOI 10.1109/81.922456 (2001)
Klein, E., Gross, N., Kopelowitz, E., Rosenbluh, M., Khaykovich, L., Kinzel, W., Kanter, I.: Public-channel cryptography based on mutual chaos pass filters. Phys. Rev. E 74(4), 046,201, DOI 10.1103/PhysRevE. 74.046201 (2006)
Klein, E., Gross, N., Rosenbluh, M., Kinzel, W., Khaykovich, L., Kanter, I.: Stable isochronal synchronization of mutually coupled chaotic lasers. Phys. Rev. E 73(6), 066,214, DOI 10.1103/PhysRevE.73.066214 (2006)
Kolumban, G., Krébesz, T.: Chaotic communications with autocorrelation receiver: Modeling, theory and performance limits. In: Kocarev, L., Galias, Z., Lian, S. (eds.) Intelligent Computing Based on Chaos, Studies in Computational Intelligence, vol. 184, pp. 121–143, Springer Berlin/Heidelberg, 10.1007/978-3-540-95972-4_6 (2009)
Kolumban, G., Kennedy, M., Chua, L.: The role of synchronization in digital communications using chaos. I. fundamentals of digital communications. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 44(10), 927–936, DOI 10.1109/81.633882 (1997)
Kolumban, G., Kennedy, M., Chua, L.: The role of synchronization in digital communications using chaos. II. chaotic modulation and chaotic synchronization. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 45(11), 1129–1140, DOI 10.1109/81.735435 (1998)
Kolumban, G., Kennedy, M., Kis, G., Jako, Z.: FM-DCSK: a novel method for chaotic communications. In: Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, 1998. ISCAS ’98. (1998)
Kolumban, G., Kennedy, M., Jako, Z., Kis, G.: Chaotic communications with correlator receivers: theory and performance limits. Proc. IEEE 90(5), 711–732, DOI 10.1109/JPROC.2002.1015003 (2002)
Kostelich, E.J., Schreiber, T.: Noise reduction in chaotic time-series data: A survey of common methods. Phys. Rev. E 48(3), 1752–1763, DOI 10.1103/PhysRevE.48.1752 (1993)
Kostelich, E.J., Yorke, J.A.: Noise reduction: Finding the simplest dynamical system consistent with the data. Phys. D Nonlinear Phenom. 41(2), 183–196, DOI 10.1016/0167-2789(90)90121-5 (1990)
Landa, P., Rosenblum, M.: Time series analysis for system identification and diagnostics. Phys. D Nonlinear Phenom. 48(1), 232–254, DOI 10. 1016/0167-2789(91)90059-I (1991)
Landsman, A.S., Schwartz, I.B.: Complete chaotic synchronization in mutually coupled time-delay systems. Phys. Rev. E 75(2), 026,201, DOI 10.1103/PhysRevE.75.026201 (2007)
Lathi, B.P.: Modern Digital and Analog Communication Systems, 4th edn. Oxford University Press, New York, NY, USA (2009)
Lau, F., Tse, C., Ye, M., Hau, S.: Coexistence of chaos-based and conventional digital communication systems of equal bit rate. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(2), 391–408, DOI 10.1109/TCSI.2003.822398 (2004)
Lau, F.C.M., Tse, C.K.: Chaos-based digital communication systems. Springer, Berlin (2003)
Lawrance, A.: Recent theory and new applications in chaos communications. In: Proceedings of 2010 IEEE International Symposium on Circuits and Systems (ISCAS) (2010)
Liu, J., Chen, H., Tang, S.: Optical-communication systems based on chaos in semiconductor lasers. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 48(12), 1475–1483, DOI 10.1109/TCSI.2001.972854 (2001)
López-Gutirrez, R., Posadas-Castillo, C., López-Mancilla, D., Cruz-Hernndez, C.: Communicating via robust synchronization of chaotic lasers. Chaos, Solitons, Fractals 42(1), 277–285, DOI 10.1016/ j.chaos.2008.11.019 (2009)
Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141, DOI 10.1175/1520-0469(1963)020⟨0130:DNF⟩2.0.CO;2 (1963)
Luengo, D., Santamaria, I.: Secure communications using OFDM with chaotic modulation in the subcarriers. In: 2005 IEEE 61st Vehicular Technology Conference, 2005. VTC 2005-Spring, vol. 2, pp. 1022–1026, DOI 10.1109/VETECS.2005.1543461 (2005)
Luengo, D., Santamaría, I., Vielva, L.: Asymptotically optimal maximum-likelihood estimator of a class of chaotic signals using the Viterbi algorithm. In: 13th European Signal Processing Conference (EUSIPCO 2005), Antalya, Turkey, pp. 1–4 (2005)
Macau, E.E.N., Marinho, C.M.P.: Communication with chaos over band-limited channels. Acta Astronautica, DOI 10.1016/S0094-5765(03)80007-3, The New Face of Space Selected Proceedings of the 53rd International Astronautical Federation Congress. 53(4-10), 465–475 (2003)
Marinho, C.M., Macau, E.E., Yoneyama, T.: Chaos over chaos: A new approach for satellite communication. Acta Astronautica, DOI 10. 1016/j.actaastro.2005.03.019, Infinite Possibilities Global Realities, Selected Proceedings of the 55th International Astronautical Federation Congress, Vancouver, Canada, 4–8 October 2004. 57(2-8), 230–238 (2005)
Mazzini, G., Setti, G., Rovatti, R.: Chaotic complex spreading sequences for asynchronous DS-CDMA. i. system modeling and results. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 44(10), 937–947, DOI 10.1109/ 81.633883 (1997)
Monteiro, L., Lisboa, A., Eisencraft, M.: Route to chaos in a third-order phase-locked loop network. Signal Process. 89(8), 1678–1682, DOI 10. 1016/j.sigpro.2009.03.006 (2009)
Murakami, A., Shore, K.A.: Chaos-pass filtering in injection-locked semiconductor lasers. Phys. Rev. A 72(5), 053,810, DOI 10.1103/ PhysRevA.72.053810 (2005)
Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice Hall, Upper Saddle River, NJ, USA (2009)
Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 64(11), 1196–1199, DOI 10.1103/PhysRevLett.64.1196 (1990)
Pantaleon, C., Luengo, D., Santamaria, I.: Optimal estimation of chaotic signals generated by piecewise-linear maps. IEEE Signal Process. Lett. 7(8), 235–237, DOI 10.1109/97.855451 (2000)
Papadopoulos, H., Wornell, G.: Optimal detection of a class of chaotic signals. IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP-93, vol. 3, pp. 117–120, DOI 10.1109/ICASSP. 1993.319449 (1993)
Pareschi, F., Setti, G., Rovatti, R.: Implementation and testing of high-speed CMOS true random number generators based on chaotic systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 57(12), 3124–3137, DOI 10.1109/TCSI.2010.2052515 (2010)
Paul, J., Lee, M.W., Shore, K.A.: Effect of chaos pass filtering on message decoding quality using chaotic external-cavity laser diodes. Opt. Lett. 29(21), 2497–2499, DOI 10.1364/OL.29.002497 (2004)
Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824, DOI 10.1103/PhysRevLett.64.821 (1990)
Rovatti, R., Setti, G., Mazzini, G.: Chaotic complex spreading sequences for asynchronous DS-CDMA. Part II. Some theoretical performance bounds. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 45(4), 496–506, DOI 10.1109/81.669073 (1998)
Rovatti, R., Mazzini, G., Setti, G.: On the ultimate limits of chaos-based asynchronous DS-CDMA-I: basic definitions and results. IEEE Transactions on Circuits and Systems I: Regular Papers, 51(7), 1336–1347, DOI 10.1109/TCSI.2004.830700 (2004)
Rulkov, N.F., Tsimring, L.S.: Synchronization methods for communication with chaos over band-limited channels. Int. J. Circ. Theor. Appl. 27, 555–567 (1999)
Sauer, T.: A noise reduction method for signals from nonlinear systems. Phys. D Nonlinear Phenom. 58(1-4), 193–201, DOI 10.1016/ 0167-2789(92)90108-Y (1992)
Soriano, D.C., Suyama, R., Attux, R.: Blind extraction of chaotic sources from white gaussian noise based on a measure of determinism. In: Adali, T., Jutten, C., Romano, J.M.T., Barros, A. (eds.) Independent Component Analysis and Signal Separation. Lecture Notes in Computer Science, vol. 5441, pp. 122–129. Springer Berlin/Heidelberg (2009)
Stavroulakis, P. (ed.): Chaos Applications in Telecommunications. CRC Press, Boca Raton, FL, USA (2005)
Syvridis, D.: Optical Chaos Encoded Communications: Solutions for Today and Tomorrow. In: 2009 IEEE LEOS Annual Meeting Conference Proceedings, Vols. 1 and 2, IEEE Photon Soc., IEEE, IEEE Lasers and Electro-Optics Society (LEOS) Annual Meeting, pp. 759–760 (2009)
Tam, W.M., Lau, F.C.M., Tse, C.K.: Digital Communications with Chaos: Multiple Access Techniques and Performance. Elsevier, NY, USA (2006)
Tavazoei, M.S., Haeri, M.: Chaos in the APFM nonlinear adaptive filter. Signal Process. 89(5), 697–702, DOI 10.1016/j.sigpro.2008.10.032 (2009)
Tsekeridou, S., Solachidis, V., Nikolaidis, N., Nikolaidis, A., Tefas, A., Pitas, I.: Statistical analysis of a watermarking system based on Bernoulli chaotic sequences. Signal Process. 81(6), 1273–1293, DOI 10. 1016/S0165-1684(01)00044-5 (2001)
Vicente, R., Mirasso, C.R., Fischer, I.: Simultaneous bidirectional message transmission in a chaos-based communication scheme. Opt. Lett. 32(4), 403–405, DOI 10.1364/OL.32.000403 (2007)
Voss, H.U.: Anticipating chaotic synchronization. Phys. Rev. E 61(5), 5115–5119, DOI 10.1103/PhysRevE.61.5115 (2000)
Wagemakers, A., Buldú, J.M., Sanjuán, M.A.F.: Experimental demonstration of bidirectional chaotic communication by means of isochronal synchronization. Europhys. Lett. 81(4), 40,005 (2008)
Wagemakers, A., Buldu, J.M., Sanjuán, M.A.F. Isochronous synchronization in mutually coupled chaotic circuits. Chaos 17(2), 023128 DOI 10.1063/1.2737820 (2007)
Williams, C.: Chaotic communications over radio channels. IEEE Trans. Circ. Syst. I. Fund. Theor. Appl. 48(12), 1394–1404, DOI 10.1109/ TCSI.2001.972846 (2001)
Wu, C.W., Chua, L.O.: A simple way to synchronize chaotic systems with applications to secure communication systems. Int. J. Bifurcat. Chaos 3(6), 1619–1627 (1993)
Xia, Y., Tse, C., Lau, F.: Performance of differential chaos-shift-keying digital communication systems over a multipath fading channel with delay spread. IEEE Transactions on Circuits and Systems II: Express Briefs, 51(12), 680–684, DOI 10.1109/TCSII.2004.838329 (2004)
Zhou, B.B., Roy, R.: Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators. Phys. Rev. E 75(2), 026,205, DOI 10.1103/PhysRevE.75.026205 (2007)
Acknowledgements
J.M.V. Grzybowski thanks FAPESP, grant nr. 2008/11684-0; M. Eisencraft and E.E.N. Macau thanks CNPq for the support on this research.
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Grzybowski, J.M.V., Eisencraft, M., Macau, E.E.N. (2011). Chaos-Based Communication Systems: Current Trends and Challenges. In: Banerjee, S., Mitra, M., Rondoni, L. (eds) Applications of Chaos and Nonlinear Dynamics in Engineering - Vol. 1. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21922-1_7
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