# End-to-End Learning of Joint Geometric and Probabilistic Constellation Shaping

arXiv: https://arxiv.org/abs/2112.05050 · HTML: https://mlsanity.com/paper/2112.05050/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Trainable Communication Systems: Concepts and Prototype](https://mlsanity.com/paper/1911.13055/) (2019)
- [An Overview on Application of Machine Learning Techniques in Optical Networks](https://mlsanity.com/paper/1803.07976/) (2018)
- [End-to-end Deep Learning of Optical Fiber Communications](https://mlsanity.com/paper/1804.04097/) (2018)
- [Nonlinear Interference Mitigation via Deep Neural Networks](https://mlsanity.com/paper/1710.06234/) (2017)
- [Joint Learning of Geometric and Probabilistic Constellation Shaping](https://mlsanity.com/paper/1906.07748/) (2019)
- [Joint Learning of Probabilistic and Geometric Shaping for Coded Modulation Systems](https://mlsanity.com/paper/2004.05062/) (2020)
- [End-to-End Learning of Geometrical Shaping Maximizing Generalized Mutual Information](https://mlsanity.com/paper/1912.05638/) (2019)
- [Deep-learning Autoencoder for Coherent and Nonlinear Optical Communication](https://mlsanity.com/paper/2006.15027/) (2020)
- [Deep Learning of Geometric Constellation Shaping including Fiber Nonlinearities](https://mlsanity.com/paper/1805.03785/) (2018)
- [End-to-End Deep Learning of Long-Haul Coherent Optical Fiber Communications via Regular Perturbation Model](https://mlsanity.com/paper/2107.12320/) (2021)

## Built on by (most cited first, 2 of 2)

- [Geometric Constellation Shaping for Fiber-Optic Channels via End-to-End Learning](https://mlsanity.com/paper/2211.04311/) (2022)
- [Friendly Attacks to Improve Channel Coding Reliability](https://mlsanity.com/paper/2401.14184/) (2024)

## Abstract (arXiv)

We present a novel autoencoder-based learning of joint geometric and probabilistic constellation shaping for coded-modulation systems. It can maximize either the mutual information (for symbol-metric decoding) or the generalized mutual information (for bit-metric decoding).