Zusammenfassung
Secure communications using chaotic waveforms has became a particular
application of nonlinear dynamics appeared at the beginning of 1990s.
For example,
electronic circuits modeled by nonlinear ordinary differential equations
were used very often for the generation of chaotic dynamics,
however, the encryption efficiency of these electronic setups is limited by
the embedded low-dimensional complexity.
Recently, Ikeda-type delay dynamics (DD) has shown to be an outstanding
candidate for chaos-based encryption in modern high speed optical
telecommunications.
It is known that the unique feature of DD is to exhibit extremely
complex chaotic behaviours, which can be quantified in terms of
Lyapunov spectrum of a given chaotic regime in a reconstructed
phase space of finite dimension, and finally a Lyapunov dimension is derived.
Dorizzi et al. had shown that the Lyapunov dimension has linear
dependence with the ratio $T/\tau$,
where $\tau$ is a characteristic response time and $T$ is the delay time.
Larger et al. experimentally demonstrated a high masking efficiency
in Ikeda-type optoelectronics
intended for practical applications, where the Lyapunov dimension
can be up to 470 when $T/\tau$ equals 60.
Chaos synchronization is widely used for the encoding and decoding
technique, in which the output of the receiver replicates the same
chaotic waveform as that in the emitter.
However, the decoding quality is strongly relied on matching conditions
between the emitter and receiver elements.
Thus, it would be interesting to ask that
Is there a possible way to directly extract message
from high-complexity encoded signals?.
In this study,
empirical mode decomposition developed by Huang et al.
is employed to decode message from
an Ikeda-type microwave system.
Under considerations of the high-dimensional chaos encryption
as well as the high masking efficiency,
it is shown that a meaningful data set embedded in chaotic fluctuations can
be directly filtered out in a reasonable way.
Our approach is quite different from the well-known encoding/decoding technique
by use of chaos synchronization.
Furthermore,
our satisfactory results suggest that
empirical mode decomposition can be generally applied to
data mining in various systems.
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