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Pulse shaping for coherent optical fiber communication has been an activearea of research for the past decade. Most of the early schemes are based onclassic Nyquist pulse shaping that was originally intended for linear channels.The best known classic scheme, the split digital back-propagation (DBP), usesjoint pre-distortion and post equalization and hence, a nonlinear transmitter(TX); it, however, suffers from spectral broadening on the fiber due to theKerr-effect. With the advent of deep learning in communications, it has beenrealized that an Autoencoder can learn to communicate efficiently over theoptical fiber channel, jointly optimizing geometric constellations and pulseshaping - while also taking into account linear and nonlinear impairments suchas chromatic dispersion and Kerr-nonlinearity. E.g., arXiv:2006.15027 shows howan Autoencoder can learn to mitigate spectral broadening due to the Kerr-effectusing a trainable linear TX. In this paper, we extend this linear architecturaltemplate to a scalable nonlinear pulse shaping consisting of a ConvolutionalNeural Network at both transmitter and receiver. By introducing a novel$\gamma$-lifting training procedure tailored to the nonlinear optical fiberchannel, we achieve stable Autoencoder convergence to pulse shapes reachinginformation rates outperforming the classic split DBP reference at high inputpowers.

Introducing $\gamma$-lifting for Learning Nonlinear Pulse Shaping in Coherent Optical Communication