Reducing the effect of noise on chaos synchronization without capping

Hilliam, Rachel and Lawrance, Anthony (2002). Reducing the effect of noise on chaos synchronization without capping. In: International Symposium on Nonlinear Theory and its Applications, Oct 7-11, Xi'an, China.


Research in electronic communications has developed chaos based modelling to enable messages to be carried by chaotic spreading sequences. When such systems are used it is necessary to simultaneously know the resulting chaotic sequence at both the transmitting and receiving stations. This is possible using the idea of synchronization providing there is no noise present in the system. When noise is present in the transmission channel, recovery of the spreading sequence may be inaccurate or even impossible and the resulting sequence may no longer lie within the chaotic map range. A usual method of dealing with this problem is to cap iterations lying outside the range at their extremes, a procedure which increases the loss of synchronization. This paper discusses how synchronization can be improved by the transformation of the spreading sequence to be transmitted; the method uses knowledge of the invariant distribution of the chaotic spreading sequence, before noise corrupts it in the transmission channel. An ‘inverse’ transformation is applied at the receiver station with the result that the noise has a reduced impact on the synchronization and also on the subsequence recovery of the message.

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