Summary
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.
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References
K. M. Cuomo and A. V. Oppenheim, Circuit implementation of synchronized chaos with applications to communications, Phys. Rev. Lett., vol. 71(1), pp. 65–68, 1993.
L. Kocarev, K. S. Halle, K. Eckert, L. O. Chua and U. Parlitz, Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurcation Chaos, vol. 2, pp. 709–713, 1992.
T. L. Carroll and L. M. Pecora, Synchronizing nonautonomous chaotic circuits, IEEE Trans. Circuits Syst., vol. 40(10), pp. 646–650, 1993.
C. W. Wu and L. O. Chua, A simple way to synchronize chaotic systems with applications to secure communication systems, Int. J. Bif. Chaos, vol. 3(6), pp. 1619–1627, 1993.
P. Colet and R. Roy, Digital communication with synchronized chaotic lasers, Optics Lett., vol. 19(24), pp. 2056–2058, 1994.
P. Celka, Chaotic synchronization and modulation of nonlinear time-delayed feedback optical systems. IEEE Trans. Circuits Syst., vol. 42(8), pp. 455–463, 1995.
P. Celka, Synchronization of chaotic optical dynamical systems through 700 m of single mode fiber. IEEE Trans. Circuits Syst., vol. 43(10), pp. 869–872, 1996.
C. R. Mirasso, P. Colet, and P. Garcia-Fernández, Photonics Technol. Lett 8, 299 (1996)
G. D. VanWiggeren and R. Roy, Communication with chaotic lasers, Science, vol. 279(5354), pp. 1198–1200, 1998.
G. D. VanWiggeren and R. Roy, Optical communication with chaotic waveforms, Phys. Rev. Lett., vol. 81(16), pp. 3547–3550, 1998.
H. D. I. Abarbanel and M. B. Kennel, Synchronizing high-dimensional chaotic optical ring dynamics, Phys. Rev. Lett., vol. 80(14), pp. 3153–3156, 1998.
G. Kolumban, G. Kis, and Z. Jákó, M. P. Kennedy. FM-DCSK: a robust modulation scheme for chaotic communications. IEICE Trans. Fundamentals of Electronics, Communication, and Computer Science, vol.E81-A(9), pp. 1798–8002, 1998.
L. M. Pecora and T. L. Carroll. Synchronization in chaotic systems. Phys. Rev. Lett., vol.64, pp. 821–824, 1990.
H. Fujisaka and T. Yamada, Stability theory of synchronized motion in coupled-oscillator systems, Prog. Theor. Phys., vol. 69(1), pp. 32–47, 1984.
L. M. Pecora and T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., vol. 64(8), pp. 821–824, 1990.
D. R. Frey, Chaotic digital encoding: an approach to secure communication, IEEE Trans. Circuits Syst., vol. 40(10), pp. 660–666, 1993.
A. R. Volkovskii and N. F. Rulkov, Synchronous chaotic response of a nonlinear oscillator system as a principle for the detection of the information component of chaos, Tech. Phys. Lett., vol. 19(2), pp. 97–99, 1993.
U. Feldmann, M. Hasler, and W. Schwarz, Communication by chaotic signals: the inverse system approach, Int. J. Ciruit Theory Appl., vol. 24(5), 1996, pp. 551–579.
L. Kocarev and U. Parlitz, General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett., vol. 74(25), pp. 5028–5031, 1995.
M. Hasler. Synchronization of chaotic systems and transmission of information. Int. J. of Bifurcation and Chaos, vol. 8(4), pp. 647–659, 1998.
T. L. Carroll and L. M. Pecora, Cascading synchronized chaotic systems. Physica D, vol. 67, pp. 126–140, 1993.
H. Dedieu, M. P. Kennedy, and M. Hasler, Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE Trans. Circuits Syst.-I, vol. 40, pp. 634–642, 1993.
K. Murali and M. Lakshmanan, Transmission of signals by synchronization in a chaotic Van der Pol-Duffing oscillator. Phys. Rev. E, vol. 48, pp. R1624–1626, 1993.
Y. H. Yu, K. Kwak, and T. K. Lim, Secure communication using small time continuous feedback. Physics Letters A, vol. 197, pp. 311–316, 1995.
K. S. Halle, C. W. Wu, M. Itoh, and L. O. Chua, Spread spectrum communication through modulation of chaos. Int. J. Bifurcation Chaos, vol. 3, pp. 469–477, 1993.
U. Parlitz and L. Kocarev, General approach for chaotic synchronization with applications to communication. Phys. Rev. Lett., vol. 74, pp. 5028–5031, 1995.
U. Parlitz, L. Kocarev, T. Stojanovski, and H. Preckel, Encoding messages using chaotic synchronization. Phys. Rev. E, vol. 53, pp. 4351–4361, 1996.
N. F. Rulkov and L. S. Tsimring. Synchronization methods for communications with chaos over band-limited channel Int. J. Circuit Theory and Applications., vol. 27, pp. 555–567, 1999.
G. Kolumban, M. P. Kennedy and L. O. Chua, The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization, IEEE Trans. Circuits Syst.-I, vol. 45(11), pp. 1129–1140, 1998.
C. Williams, Chaotic communication over radio channels, IEEE Trans. Circuits Syst.-I, vol. 48(12), pp. 1394–1404, 2001.
T. L. Carroll, Amplitude-independent chaotic synchronization. Phys. Rev. E, vol. 53(4A), pp. 3117–3122, 1996.
T. L. Carroll and G. A. Johnson, Synchronizing broadband chaotic systems to narrow-band signals, Phys. Rev. E, vol. 57(2), pp. 1555–1558, 1998.
E. Rosa, S. Hayes, and C. Grebogi, Noise filtering in communication with chaos. Phys. Rev. Lett., vol. 78(7), pp. 1247–1250, 1997.
N. F. Rulkov and A. R. Volkovskii, Threshold synchronization of chaotic relaxation oscillations, Physics Letters A, vol. 179(4–5), pp. 332–336, 1993.
H. Torikai, T. Saito, and W. Schwartz, Synchronization via multiplex pulse trains, IEEE Trans. Circuits Syst.-I, vol. 46(9), 1072–1085, 1999.
T. L. Carroll, Communicating with use of filtered, synchronized, chaotic signals, IEEE Trans. Circuits Syst.-I, vol. 42(2), pp. 105–110, 1995.
T. L. Carroll, Noise-robust synchronized chaotic communication, IEEE Trans. Circuits Syst.-I, vol. 48(12), pp. 1519–1522, 2001.
N. F. Rulkov and A. R. Volkovskii. Synchronization of pulse-coupled chaotic oscillators. In Proc. of the 2nd Experimental Chaos Conference, pp. 106–115, World Scientific, 1993.
M. M. Sushchik et al. Chaotic Pulse Position Modulation: a Robust Method of Communicating with Chaos IEEE Communications Letters, vol.4, pp. 128–130, 2000.
M. Z. Win and R. A. Scholtz. Impulse radio: how it works. IEEE Communications Letters, vol.2(2), pp.36–38, 1998.
T. Yang and L. O. Chua. Chaotic impulse radio: A novel chaotic secure communication system. Int. J. of Bifurcation and Chaos, vol.10, pp. 345–357, 2000.
P. A. Bernhardt Coupling of the relaxation and resonant elements in the autonomous chaotic relaxation oscillator (ACRO) Chaos vol.2, 183–199, 1992.
N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, and A. R. Volkovskii Digital Communication Using Chaotic-Pulse-Position Modulation. IEEE Trans. Circuits Syst. vol. 48, pp. 1436–1444, 2001.
N. F. Rulkov, M. A. Vorontsov and L. Illing Chaotic Free-Space Laser Communication over Turbulent Channel. Phys. Rev. Lett. vol. 89, 277905, 2002.
L. C. Andrews, R. L. Phillips, and C. Y. Hopen, Laser Beam Scintillation with Applications (SPIE Press, Bellingham, 2001).
T. Stojanovski, Lj. Kocarev, and R. Harris. Applications of symbolic dynamics in chaos synchronization. IEEE Trans. Circuit. Syst. I, vol.44(10), pp. 1014–1017, 1997.
H. Torikai, T. Saito, and W. Schwarz. Multiplex communication scheme based on synchronization via multiplex pulse-trains. In Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, pp. 554–557, New York, 1998.
H. Torikai, T. Saito, and W. Schwarz. Synchronization via multiplex pulsetrains. IEEE Trans. Circuit. Syst. I, vol.46(9), pp.1072–1085, 1999.
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Rulkov, N.F., Volkovskii, A.R., Sushchik, M.M., Tsimring, L.S., Illing, L. (2006). Digital Communication Using Self-Synchronizing Chaotic Pulse Position Modulation. In: Larson, L.E., Tsimring, L.S., Liu, JM. (eds) Digital Communications Using Chaos and Nonlinear Dynamics. Institute for Nonlinear Science. Springer, New York, NY . https://doi.org/10.1007/0-387-29788-X_2
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DOI: https://doi.org/10.1007/0-387-29788-X_2
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