  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.
