Transmitter optimization and theoretical bounds for dispersion-limited optical fiber links

In this paper, we present a novel mathematical investigation on the dispersion-limited optical communication channel. We tackle the problem using a comprehensive approach that is based on the optimization of the energy transfer from the input to the output of the channel. We solve the optimization problem deriving a fundamental integral equation, which we are able to solve analytically. We show that the dispersion-limited optical channel has a very interesting equivalence to the ideal lowpass filter. This equivalence allows us to derive new bounds on the maximum achievable bit rate on the channel with limited intersymbol interference (ISI). In particular, we demonstrate that by suitably increasing the memory of the modulator and using the optimal pulses derived in this paper, one can transmit with limited ISI over a channel with arbitrarily high dispersion.