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Chaos Communication Performance: Theory and Computation

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Abstract

In this paper new and existing approaches are developed to compute the bit-error rate for chaos-based communication systems. The multi-user coherent antipodal chaos shift keying system is studied and evaluated in its coherent form, in the sense of perfect synchronisation between transmitted and received chaotic sequences. Transmission is through an additive white Gaussian noise channel. Four methods are interrelated in the paper, three approximate ones and an exact one. The least accurate but most well known is based on simple Gaussian approximation; this is generalised to better reveal its structure. Two accurate and computationally efficient approximate methods are based on conditional Gaussian approximation and the statistical distribution of the typically non-constant bit energy. The most insightful but computationally expensive one is based on exact theory and rests on explicit mathematical results for particular chaotic maps used to spread binary messages. Both upper and lower bounds to the bit-error rate are suggested. The relative advantages of the different approaches are illustrated with plots of bit-error rate against signal to noise ratio.

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Authors and Affiliations

  1. LACIME Laboratory, École de Technologie Supérieure, Université du Québec, 1100, rue Notre-Dame Ouest, Montréal, QC, H3C 1K3, Canada

    G. Kaddoum

  2. Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK

    Anthony J. Lawrance

  3. LATTIS/INSA, University of Toulouse, 135 Avenue de Rangueil, 31071, Toulouse cedex 7, France

    P. Chargé

  4. CNAM Paris, LAETITIA Laboratory, 292 rue Saint-Martin, 75003, Paris, France

    D. Roviras

Authors
  1. G. Kaddoum
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  2. Anthony J. Lawrance
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  3. P. Chargé
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  4. D. Roviras
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Correspondence to Anthony J. Lawrance.

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Kaddoum, G., Lawrance, A.J., Chargé, P. et al. Chaos Communication Performance: Theory and Computation. Circuits Syst Signal Process 30, 185–208 (2011). https://doi.org/10.1007/s00034-010-9217-1

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  • DOI: https://doi.org/10.1007/s00034-010-9217-1

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