# High-Cardinality Hybrid Shaping for 4D Modulation Formats in Optical Communications Optimized via End-to-End Learning

arXiv: https://arxiv.org/abs/2112.10471 · HTML: https://mlsanity.com/paper/2112.10471/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Artificial Neural Networks for Photonic Applications: From Algorithms to Implementation](https://mlsanity.com/paper/2408.02685/) (2024)

## Abstract (arXiv)

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%.