Fundamental dispersion limit for spectrally bounded On-Off-Keying communication channels

The fundamental dispersion limit for optical communication based the On-Off-Keying format is calculated. It is shown both analytically and with numerical simulations that an OOK optical sequence, which passes through spectrally narrow noncompensated dispersive channel cannot exceed the limit 1/{\pi} > {\beta_2} L B^2, where {\beta_2}, L and B are the dispersion coefficient, the fiber's length and the bit-rate respectively. To the best of our knowledge, this is the first time that such a fundamental limit was formulated. In the literature, only approximation evaluations were developed yielding much smaller limiting values.