  Optimizing modulation and detection strategies for a given channel is
critical to maximize the throughput of a communication system. Such an
optimization can be easily carried out analytically for channels that admit
closed-form analytical models. However, this task becomes extremely challenging
for nonlinear dispersive channels such as the optical fiber. End-to-end
optimization through autoencoders (AEs) can be applied to define
symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings,
but so far it has been mainly shown for systems relying on approximate channel
models. Here, for the first time, we propose an AE scheme applied to the full
optical channel described by the nonlinear Schr\{"o}dinger equation (NLSE).
Transmitter and receiver are jointly optimized through the split-step Fourier
method (SSFM) which accurately models an optical fiber. In this first numerical
analysis, the detection is performed by a neural network (NN), whereas the
symbol-to-waveform mapping is aided by the nonlinear Fourier transform (NFT)
theory in order to simplify and guide the optimization on the modulation side.
This proof-of-concept AE scheme is thus benchmarked against a standard
NFT-based system and a threefold increase in achievable distance (from 2000 to
6640 km) is demonstrated.
