Abstract
This work shows that chaotic signals with different power spectrum and different positive Lyapunov exponents are robust to linear superposition, meaning that the superposition preserves the Lyapunov exponents and the information content of the source signals, even after being transmitted over non-ideal physical medium. This work tackles with great detail how chaotic signals and their information content are affected when travelling through medium that presents the non-ideal properties of multi-path propagation, noise and chaotic interference (linear superposition), and how this impacts on the proposed communication system. Physical media with other non-ideal properties (dispersion and interference with periodic signals) are also discussed. These wonderful properties that chaotic signals have allow me to propose a novel communication system based on chaos, where information composed from and to multiple users each operating with different base frequencies and that is carried by chaotic wavesignals, can be fully preserved after transmission in the open air wireless physical medium, and it can be trivially decoded with low probability of errors.
Highlights
Communication systems are designed to cope with the constraints of the physical medium
This paper focuses on information signals that are linearly composed, and this approach could in principle be used to explain communication in neurons doing electric synapses
I show with mathematical rigour that a linear superposition of chaotic signals with different natural frequencies fully preserves the spectra of Lyapunov exponents and the information content of the source signals
Summary
Communication systems are designed to cope with the constraints of the physical medium. Chaos for communication that the information content carried by the composed signal r (t) can be trivially decomposed, or decoded, by a simple threshold (see Eq (18)), with low probability of errors, or no errors at all for sufficiently small noise levels. In the latter case, that would imply that the information encoding capacity provides the information capacity of the system, or the rate of information received/decoded.
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