Complete Replacement of Chaotic Uncertainty with Transmitted Information
Matthew B. Kennel · AIP conference proceedings · 2003
It is now well known that chaotic systems may be controlled with small perturbations to execute orbits yielding a specified symbolic itinerary as long as the grammatical rules of those transitions are allowed by the natural dynamical system. Here, we employ techniques taken from contemporary data compression technology (source modeling and arithmetic coding) but reverse their usual roles to create a channel coder tuned to the observed natural dynamics. With a universal compression technique, we estimate a variable depth Markov‐chain model which faithfully approximates the observed symbolic dynamics of the uncontrolled electronic circuit source. Subsequently, we drive the experimental system to the itinerary generated from an arbitrary white binary stream (the message) encoded using the symbolic model and the arithmetic coder. The transmitter’s orbits are indistinguishable in grammar and measure from the uncontrolled attractor, demonstrating chaotic stegeanography with no rate loss. All the information naturally generated from chaos has been replaced by message bits at the same rate. Transmission on other chaotic saddles are accessible as well: the measure on the Markov chain may be modified arbitrarily as long as the topology is still respected. One particularly interesting solution, which is derived in explicit form, is that saddle which yields an entropy rate equal to the channel capacity, the upper bound for the given topology. Our algorithms are general, working as stated for arbitrary finite‐depth grammars and alphabets, without analytical foreknowledge of the transmitter’s equations of motion, though a good symbolic partition is necessary.