• Channel Capacity
• Nonlinear optical channel
• Mutual Information
• Fiber optic telecommunicaitions

One important topic related to the future of the Optical Telecommunication
field is the the determination of a limit in the maximum
information rate for the general optical channel.
This limit has been already determined in the past by relying
on the concept of channel capacity from Claude Shannon that
is nowadays one of the most useful measure to characterize a
communication medium.
The possibility to determine such value is essential both practically,
for the design of optimal optical system in terms of efficiency and complexity, and it’s also important theoretically to determine a fundamental limit above which nothing can be
done to go further.
In contrast to what concern the other famous example of
physical channels used to convey information (i.e. wireless,
copper,..) that are described by linear equations for which analytical
solutions exist, for the optical channel it is not that easy.
In particular if we talk about long-haul systems or for any system in which high intensity signals are required, the opticalfiber begins to exhibit non-linear effects (the so called Kerr nonlinearities,
that are considered negligible at low power). In such regime the medium is described by a well known stochastic partial differential equation called generalized Schroedinger equation, for which an analytical solution is not known. Up to now the capacity of the channel (in the Shannon sense) as been evaluated just in the linear regime of the medium and no accurate limits has been found yet for the general case. In this context a way for the estimation of the channel capacity and so of the bound to the information rate transmittable in the channel, consists in employing the very fundamental concept of mutual information, appertaining to the field of Information Theory.
It has been proved that a tight link between mutual information, entropy and capacity exists and wide range of studies exist for their estimation.
Furthermore, to the best of our knowledge, a very limited number of this estimation methods has been applied to the field of optical telecommunication with the above stated goal.
In the following work we’ll analyse a set of non parametric estimation techniques, ranging from the most famous and known to the most recent ones, with the goal of finding an accurate way of estimating the capacity of the non-linear optical
channel.