A chaotic system that communicates through unlimited propagation losses and/or transmitter gain

A noise-like appearance and sensitive dependence on initial conditions render communications based on chaos secure. The sensitivity of chaotic processes to amplitude variations, however, presents synchronization problems that historically have severely limited communications distances. A chaotic communications system is presented that detects, and corrects for signal levels that deviate from the receiver optimal design values. It operates successfully with unlimited transmitter amplification and/or propagation losses, in the presence of noise. The system is described, and results shown for 80 dB loss through 20 dB gain without encountering algorithmic limits, in conjunction with 40 dB signal-to noise ratio (SNR) through 0 dB SNR