The seemingly random behavior of chaotic phenomena would appear to have little to do with the ordered discipline required to send a sequence of 0s and 1s in a way that can be accurately and reliably received. But researchers in Europe are doing just that: communicating with chaos. In November, they announced that they had used chaos to send digital messages at gigabit-per-second speeds over 115 kilometers of commercial optical fiber beneath the streets of Athens, Greece.
"It's interesting, because they did it through a commercial fiber system for the first time," says Rajarshi Roy, director of the Institute for Physical Science at the University of Maryland, in College Park.
The demonstration, performed by a pan-European team led by Apostolos Argyris of the University of Athens, depended on a somewhat counterintuitive property of chaotic systems: although they look disorganized, the systems are somewhat predictable. Take, for example, the Lorenz Attractor [see picture], a plot of the simultaneous evolution of three differential equations, discovered in the early 1960s by meteorologist Edward N. Lorenz at the Massachusetts Institute of Technology, Cambridge. The attractor consists of two lobes around which the plot continually traces, creating a butterfly shape. At any time, the trace is in either one lobe or the other.
A salient feature of chaotic systems is that their long-term behavior is often impossible to predict but their near-term behavior is quite easy to anticipate, so their immediate evolution can be controlled. By nudging the equations in a Lorenz system just so, the system trace can be sent into one butterfly wing or the other.
In the mid-1980s, Louis Pecora, at the Naval Research Laboratory, in Washington, D.C., suggested that this phenomenon could be used for communication. By labeling one lobe of the attractor "0" and the other "1," a Lorenz Attractor can be made to spell out any digital message. All that the receiver of a chaotic message requires is an identical Lorenz Attractor synchronized to the first.
When the attractors are synchronized, they effectively become part of the same chaotic circuit. The receiver--let's call him Bob, using a convention from quantum encryption--sees the attractor evolve exactly as the transmitter--let's say, Alice--intends. For example, Alice can make a small change to the chaotic circuit that sends the trace into, say, the left-hand lobe a short time later. Bob notes which lobe the plot is in and translates this into a 0 or a 1, according to the convention agreed upon with Alice earlier. By continually nudging the circuit in this way, Alice can spell out a message for Bob.
Alternatively, a method can be used that's somewhat similar to FM radio transmission. In this approach, a message is embedded on a carrier wave, but the wave in this case is chaotic rather than sinusoidal. Retrieving the message is simply a question of subtracting the carrier wave from the transmitted signal.
But why bother with chaotic communication when the telecommunications industry manages perfectly well with conventional systems? One of the advantages is that it is often easier to generate robust, high-power chaotic signals than conventional ones. In the Athens demonstration, the researchers used light from commercially available laser diodes, and the transmissions proved remarkably sturdy. Data were lost at a rate of only 1 bit in every 10 million sent at gigabit speeds. (Team leader Argyris says the bit rate was limited by his equipment rather than by the technique itself.)
A chaotic signal is also harder for an eavesdropper to identify because it is difficult to distinguish from background noise. If, besides camouflaging the communication, higher levels of privacy are needed, any Lorenzian message can be easily encrypted using standard methods of cryptography, such as public key systems.
As it happens, there is growing evidence that nature may also employ chaos to send information. Could a better understanding of chaotic communication give neuroscientists a new way to understand how living organisms transmit signals through nerves? Besides allowing for the more secure exchange of data, says Roy, the European work could provide "new insight into living systems."