Chaos communication synchronization: Combatting noise by distribution transformation

Hilliam, Rachel M and Lawrance, Anthony J (2005). Chaos communication synchronization: Combatting noise by distribution transformation. Statistics and Computing, 15(1) pp. 43–52.

DOI: https://doi.org/10.1007/s11222-005-4788-6

Abstract

Research in electronic communications has developed chaos-based modelling to enable messages to
be carried by chaotic broad-band spreading sequences. When such systems are used it is necessary
to simultaneously know the spreading sequence at both the transmitting and receiving stations. This
is possible using the idea of synchronization with bivariate maps, providing there is no noise present
in the system. When noise is present in the transmission channel, recovery of the spreading sequence
may be degraded or impossible. Once noise is added to the spreading sequence, the result may no
longer lie within the boundary of the chaotic map. A usual and obvious method of dealing with this
problem is to cap iterations lying outside the bounds at their extremes, but the procedure amplifies
loss of synchronization. With a minimum of technical details and a computational focus, this paper
first develops relevant dynamical and communication theory in the bivariate map context, and then
presents a better way of improving synchronization by distribution transformation. The transmission
sequence is transformed, using knowledge of the invariant distribution of the spreading sequence, and
before noise corrupts the signal in the transmission channel. An ‘inverse’ transformation can then be
applied at the receiver station so that the noise has a reduced impact on the recovery of the spreading
sequence and hence its synchronization. Statistical simulations illustrating the effectiveness of the
approach are presented.

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