In this paper we carry out a joint optimization of probabilistic (PS) and geometric shaping (GS) for four-dimensional (4D) modulation formats in long-haul coherent wavelength division multiplexed (WDM) optical fiber communications using an auto-encoder framework. We propose a 4D 10 bits/symbol constellation which we obtained via end-to-end deep learning over the split-step Fourier model of the fiber channel. The constellation achieved 13.6% reach increase at a data rate of approximately 400 Gbits/second in comparison to the ubiquitously employed polarization multiplexed 32-QAM format at a forward error correction overhead of 20%.
@article{arxiv.2112.10471,
title = {High-Cardinality Hybrid Shaping for 4D Modulation Formats in Optical Communications Optimized via End-to-End Learning},
author = {Vinícius Oliari and Boris Karanov and Sebastiaan Goossens and Gabriele Liga and Olga Vassilieva and Inwoong Kim and Paparao Palacharla and Chigo Okonkwo and Alex Alvarado},
journal= {arXiv preprint arXiv:2112.10471},
year = {2021}
}