Signal extraction from chaotic communications

This paper will consider the use of nonlinear dynamic (NLD) forecasting to extract messages from chaotic communication systems. Earlier work has shown that one-step prediction methods have sometimes been able to reveal the presence of hidden messages as well as the frequency content of the hidden messages. However, recovery of the actual hidden message usually involved filtering in the frequency domain. In this paper we show that it may be possible to extract the hidden message signal without filtering in the frequency domain. The approaches which will be discussed involve either the use of multi step predictions or a resumming process on the residuals after one-step prediction. For the multi step methods, two related approaches will be used. The first is primarily applicable to periodic signals, and will use the frequency information from one-step predictions to determine a block size to use for multi step predictions. The second will attempt dynamic detection of message signals using a windowed measure of the prediction error. For the resumming approach, it will be shown that even a lowest-order approximation can lead to faithful extraction of the hidden message signal for a ramping message signal that proved difficult in earlier work. These approaches will be applied to simple examples of communication schemes using signal masking and modulated chaos.