Low-complexity geometric shaping
Journal article, 2021

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 overcome these challenges, in this article, we study lattice-based geometrically shaped modulation formats in multidimensional Euclidean space. We describe and evaluate fast and low complexity modulation and demodulation algorithms that make these modulation formats practical, even with extremely high constellation sizes with more than 1028 points. The uncoded bit error rate performance of these constellations is compared with the conventional quadrature amplitude modulate (QAM) formats in the additive white Gaussian noise and nonlinear fiber channels. At a spectral efficiency of 2 bits/sym/polarization, compared with 4-QAM format, transmission reach improvement of more than 38% is shown at the hard-decision forward error correction threshold of 2.26×10−4 .


geometric shaping

Optical communication

coherent receiver

multidimensional modulation format


Ali Mirani

Chalmers, Microtechnology and Nanoscience (MC2), Photonics

Erik Agrell

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

Magnus Karlsson

Chalmers, Microtechnology and Nanoscience (MC2), Photonics

Journal of Lightwave Technology

0733-8724 (ISSN)

Vol. 39 2 363-371

Coupled fiber optic channels

Swedish Research Council (VR), 2019-12-01 -- 2023-11-30.

Signal shaping in optical communications—Beyond the Gaussian channel

Swedish Research Council (VR), 2018-01-01 -- 2021-12-31.

Subject Categories


Atom and Molecular Physics and Optics

Condensed Matter Physics



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