Communication waveform properties of an exact folded-band chaotic oscillator

• We compare an exact folded-band chaotic oscillation with an on–off keyed waveform.
• We identify two key differences between chaos and an ideal on–off keying waveform.
• The first difference is an inherent form of intersymbol interference.
• The second is a grammar restriction giving rise to a built-in variable length code.
• Analytic bounds on the error rate in receiving code letters are derived.

We interpret the waveform of an exact folded-band oscillator as an on–off keyed communication waveform. Unlike most nonlinear systems, this oscillator has a general analytic solution that allows for unusually exact analysis. Using this solution, we identify the key differences between a deterministic chaotic oscillation and an ideal on–off keying waveform to be (1) an inherent form of intersymbol interference and (2) a grammar restriction giving rise to a built-in variable length code. We define a simple coherent receiver based on a matched filter, and consider transmission in the presence of additive white Gaussian noise. Analytic expressions for upper and lower bounds on the probability of errors in receiving code letters are derived and shown to be consistent with numerical simulations.