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  • Tasev, Zarko  (10)
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Language
Year
  • 1
    Language: English
    In: IEEE Transactions on Information Theory, April, 2006, Vol.52(4), p.1366(19)
    Description: Iterative decoding algorithms may be viewed as high-dimensional nonlinear dynamical systems, depending on a large number of parameters. In this work, we introduce a simplified description of several iterative decoding algorithms in terms of the a posteriori average entropy, and study them as a function of a single parameter that closely approximates the signal-to-noise ratio (SNR). Using this approach, we show that virtually all the iterative decoding schemes in use today exhibit similar qualitative dynamics. In particular, a whole range of phenomena known to occur in nonlinear systems, such as existence of multiple fixed points, oscillatory behavior, bifurcations, chaos, and transient chaos are found in iterative decoding algorithms. As an application, we develop an adaptive technique to control transient chaos in the turbo-decoding algorithm, leading to a substantial improvement in performance. We also propose a new stopping criterion for turbo codes that achieves the same performance with considerably fewer iterations. Index Terms--Bifurcation theory, chaos, dynamical systems, iterative decoding, low-density parity-check codes, product codes, turbo codes.
    Keywords: Chaos Theory -- Analysis ; Bifurcation Theory -- Analysis ; Entropy (Information theory) -- Analysis
    ISSN: 0018-9448
    E-ISSN: 15579654
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  • 2
    Language: English
    In: Physical review. E, Statistical, nonlinear, and soft matter physics, April 2002, Vol.65(4 Pt 2A), pp.046215
    Description: We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox.
    ISSN: 1539-3755
    E-ISSN: 15502376
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  • 3
    Language: English
    In: Physical Review Letters, 7/1997, Vol.79(1), pp.51-54
    Description: A general approach for synchronizing pairs of unidirectionally coupled partial differential equations (PDEs) with spatiotemporally chaotic dynamics is introduced. We show that for a large class of PDEs, a pair of PDEs can be synchronized by driving the response system only at a finite number of space points. We also discuss the relevance of our results for control of spatiotemporal chaos.
    Keywords: Physics;
    ISSN: 0031-9007
    E-ISSN: 1079-7114
    Source: American Physical Society (APS) (via CrossRef)
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  • 4
    Language: English
    In: International Journal of Bifurcation and Chaos, 03/2004, Vol.14(03), pp.1147-1153
    Description: We suggest a link between coding theory (iterative algorithms) and chaos theory. A whole range of phenomena known to occur in nonlinear systems, like the existence of multiple fixed points, oscillatory behavior, bifurcations, chaos and transient chaos are found in turbo-decoding algorithms. We develop a simple technique to control transient chaos in turbo-decoding algorithms and improve the performance of the classical turbo codes.
    Keywords: Chaos ; turbo code ; control of chaos;
    ISSN: 0218-1274
    E-ISSN: 1793-6551
    Source: CrossRef
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  • 5
    Language: English
    In: International Journal of Bifurcation and Chaos, March 2004, Vol.14(3), pp.1147-1153
    Description: We suggest a link between coding theory (iterative algorithms) and chaos theory. A whole range of phenomena known to occur in nonlinear systems, like the existence of multiple fixed points, oscillatory behavior, bifurcations, chaos and transient chaos are found in turbo-decoding algorithms. We develop a simple technique to control transient chaos in turbo-decoding algorithms and improve the performance of the classical turbo codes.
    Keywords: Chaos ; Turbo Code ; Control of Chaos ; Engineering ; Sciences (General)
    ISSN: 0218-1274
    E-ISSN: 1793-6551
    Source: World Scientific Publishing Co.
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  • 6
    Language: English
    In: Chaos, Solitons and Fractals, 2003, Vol.15(2), pp.319-326
    Description: Chaotic pulse position modulation (CPPM) is a novel technique to communicate with chaotic signals based upon pulse trains in which the intervals between two pulses are determined by chaotic dynamics of a pulse generator. Using numerical simulations we show that CPPM offers excellent multi-path performance. We simulated the CPPM radio system, which is designed for a WLAN application and operates in the 2.4 GHz ISM frequency band with IEEE 802.11 compliant channel spacing. In this case, the average performance loss due the multi-path for CPPM is less than 5 dB.
    Keywords: Sciences (General) ; Mathematics
    ISSN: 0960-0779
    E-ISSN: 1873-2887
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  • 7
    Language: English
    In: Chaos: An Interdisciplinary Journal of Nonlinear Science, December 1997, Vol.7(4), pp.635-643
    Description: We show analytically and numerically that a pair of uni-directionally coupled spatially extended systems can synchronize. For the case of partial differential equations the synchronization can be achieved by applying the scalar driving signals only at finite number of space points. Our approach is very general and can be useful for practical applications since the synchronization is achieved via feeding in the response system only the information from certain (discrete) spatial locations of the drive system. We also stress some open problems in the field of synchronization of spatiotemporal chaos.
    Keywords: Sciences (General) ; Physics;
    ISSN: 1054-1500
    E-ISSN: 1089-7682
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  • 8
    Language: English
    In: International Journal of Bifurcation and Chaos, 04/2000, Vol.10(04), pp.869-873
    Description: The synchronization properties of a pair of Kuramoto–Sivashinsky equations are examined using only a finite number of coupling signals that are given in terms of local spatial averages. The dependence of the synchronization on the number of coupling signals and the width of the spatial average intervals is examined, including spatiotemporal intermittency of the synchronization error near the onset of synchronization.
    ISSN: 0218-1274
    E-ISSN: 1793-6551
    Source: CrossRef
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  • 9
    Language: English
    In: International Journal of Bifurcation and Chaos, December 1999, Vol.9(12), pp.2265-2270
    Description: We investigate the problem of synchronizing and controlling spatially extended systems. For this purpose a coupling scheme is introduced, that allows to synchronize and control the dynamics with only a few driving signals which are spatial averages of local regions. We estimate the optimal arrangement of the coupling signals and compare them with their usual periodic arrangement. The application in controlling, e.g. suppression of chaos, is demonstrated.
    Keywords: Engineering ; Sciences (General)
    ISSN: 0218-1274
    E-ISSN: 1793-6551
    Source: World Scientific Publishing Co.
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  • 10
    Language: English
    In: International Journal of Bifurcation and Chaos, April 2000, Vol.10(4), pp.869-873
    Description: The synchronization properties of a pair of Kuramoto–Sivashinsky equations are examined using only a finite number of coupling signals that are given in terms of local spatial averages. The dependence of the synchronization on the number of coupling signals and the width of the spatial average intervals is examined, including spatiotemporal intermittency of the synchronization error near the onset of synchronization.
    Keywords: Engineering ; Sciences (General)
    ISSN: 0218-1274
    E-ISSN: 1793-6551
    Source: World Scientific Publishing Co.
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