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This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical…

Information Theory · Computer Science 2022-09-19 Eric Sillekens , Gabriele Liga , Domaniç Lavery , Polina Bayvel , Robert I. Killey

A new geometric shaping method is proposed, leveraging unsupervised machine learning to optimize the constellation design. The learned constellation mitigates nonlinear effects with gains up to 0.13 bit/4D when trained with a simplified…

Information Theory · Computer Science 2018-05-11 Rasmus T. Jones , Tobias A. Eriksson , Metodi P. Yankov , Darko Zibar

In this paper, an unsupervised machine learning method for geometric constellation shaping is investigated. By embedding a differentiable fiber channel model within two neural networks, the learning algorithm is optimizing for a geometric…

In this paper, we present a general framework of designing geometrically shaped constellations for short-packet visible light communications with a peak- and an average-intensity constraints. By leveraging tools from large deviation theory,…

Information Theory · Computer Science 2024-04-30 Jia-Ning Guo , Ru-Han Chen , Jian Zhang , Longguang Li , Xu Yang , Jing Zhou

A simple geometric shaping method is proposed for optical wireless communication systems based on intensity modulation and direct detection (IM/DD) from an information-theoretic perspective. Constellations consisting of equiprobable levels…

Information Theory · Computer Science 2024-12-03 Suhua Zhou , Tianqi Li , Zhaoxi Fang , Jing Zhou , Wenyi Zhang

This paper proposes a simple and effective method for constructing higher-order three-dimensional (3D) signal constellations, aiming to enhance the reliability of digital communication systems. The approach systematically extends the…

Signal Processing · Electrical Eng. & Systems 2025-11-17 Sukhsagar , Nagendra Kumar , Ambuj Kumar Mishra , Vimal Bhatia , Ondrej Krejcar

Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual…

Information Theory · Computer Science 2025-06-23 Shrinivas Chimmalgi , Laurent Schmalen , Vahid Aref

The choice of constellations largely affects the performance of communication systems. When designing constellations, both the locations and probability of occurrence of the points can be optimized. These approaches are referred to as…

Information Theory · Computer Science 2019-08-30 Maximilian Stark , Fayçal Ait Aoudia , Jakob Hoydis

Constellation shaping is reviewed and revised for a WDM unrepeated system with high spectral efficiency. It is shown that for a constellation size-constrained system, previous optimization techniques can be highly sub-optimal, and a…

Optimization and Control · Mathematics 2019-11-06 Metodi P. Yankov

In this paper we propose constellations with suitable structure which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. We also demonstrate how these structured constellations…

Optimization and Control · Mathematics 2007-05-23 Guangyue Han , Joachim Rosenthal

Constellation shaping is an energy-efficient strategy involving the transmission of lower-energy signals more frequently than higher-energy signals. Previous work has shown that shaping is particularly effective when used with coded…

Information Theory · Computer Science 2012-10-18 Xingyu Xiang , Matthew C. Valenti

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To…

Signal Processing · Electrical Eng. & Systems 2024-01-25 Ali Mirani , Erik Agrell , Magnus Karlsson

In this paper, we propose a geometric shaping (GS) strategy to design 8, 16, 32 and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised…

Information Theory · Computer Science 2021-02-03 Hubert Dzieciol , Gabriele Liga , Eric Sillekens , Polina Bayvel , Domaniç Lavery

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Numerical Analysis · Mathematics 2016-01-13 Sharif Rahman , Xuchun Ren , Vaibhav Yadav

The geometry of dual-polarization four-dimensional constellations is optimized in the optical fiber channel using a recent nonlinear interference model. A 0.27 bit/4D rate gain and 13% reach increase are attained compared to…

Signal Processing · Electrical Eng. & Systems 2021-10-25 Gabriele Liga , Bin Chen , Alex Alvarado

Autoencoder-based deep learning is applied to jointly optimize geometric and probabilistic constellation shaping for optical coherent communication. The optimized constellation shaping outperforms the 256 QAM Maxwell-Boltzmann probabilistic…

Signal Processing · Electrical Eng. & Systems 2022-04-18 Vladislav Neskorniuk , Andrea Carnio , Domenico Marsella , Sergei K. Turitsyn , Jaroslaw E. Prilepsky , Vahid Aref

A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a…

Astrophysics · Physics 2009-06-11 S. Bonazzola , E. Gourgoulhon , J. -A. Marck

Autoencoder-based geometric shaping is proposed that includes optimizing bit mappings. Up to 0.2 bits/QAM symbol gain in GMI is achieved for a variety of data rates and in the presence of transceiver impairments. The gains can be harvested…

Information Theory · Computer Science 2019-07-22 Rasmus T. Jones , Metodi P. Yankov , Darko Zibar

Achievable information rates are used as a metric to design novel modulation formats via geometric shaping. The proposed geometrically shaped 256-ary constellation achieves SNR gains of up to 1.18 dB.

Information Theory · Computer Science 2020-06-05 Bin Chen , Chigo Okonkwo , Hartmut Hafermann , Alex Alvarado

Model fitting is frequently used to determine the shape of galaxies and the point spread function, for examples, in weak lensing analyses or morphology studies aiming at probing the evolution of galaxies. However, the number of parameters…

Cosmology and Nongalactic Astrophysics · Physics 2012-10-03 Guoliang Li , Bo Xin , Wei Cui
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