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Optimizing the input probability distribution of a discrete-time channel is a standard step in the information-theoretic analysis of digital communication systems. Nevertheless, many practical communication systems transmit uniformly and…

Signal Processing · Electrical Eng. & Systems 2024-12-13 Mohammad Taha Askari , Lutz Lampe

Constellation shaping is a well-established method to improve upon a regular quadrature amplitude modulation (QAM). It is known that the gain achieved by any shaping method for an additive white Gaussian noise (AWGN) channel is…

Information Theory · Computer Science 2025-04-28 Kirill Ivanov , Wei Yang , Jing Jiang

We generalize probabilistic amplitude shaping (PAS) with binary codes to the case of non-binary codes defined over prime finite fields. Firstly, we introduce probabilistic shaping via time sharing where shaping applies to information…

Information Theory · Computer Science 2017-01-30 Joseph J. Boutros , Fanny Jardel , Cyril Méasson

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

The interplay of shaped signaling and fiber nonlinearities is reviewed in the asymptotic and finite-length regime. We present explanations and discuss implications of an optimum shaping length of just a few hundred symbols.

Signal Processing · Electrical Eng. & Systems 2020-06-23 Tobias Fehenberger

We introduce a trainable coded modulation scheme that enables joint optimization of the bit-wise mutual information (BMI) through probabilistic shaping, geometric shaping, bit labeling, and demapping for a specific channel model and for a…

Information Theory · Computer Science 2020-04-15 Fayçal Ait Aoudia , Jakob Hoydis

Probabilistic constellation shaping (PCS) offers a significant performance improvement over uniform signaling. It was recently discovered that long blocks are not required to achieve maximum shaping gain when transmitting over the nonlinear…

Signal Processing · Electrical Eng. & Systems 2020-12-15 Tobias Fehenberger , Helmut Griesser , Jörg-Peter Elbers

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

Utilizing the multi-dimensional (MD) space for constellation shaping has been proven to be an effective approach for achieving shaping gains. Despite there exists a variety of MD modulation formats tailored for specific optical transmission…

Signal Processing · Electrical Eng. & Systems 2025-06-23 Bin Chen , Zhiwei Liang , Yi Lei , JingXin Deng , Shen Li , Gabriele Liga

We present an autoregressive end-to-end learning approach for probabilistic shaping on nonlinear fiber channels. Our proposed scheme learns the joint symbol distribution and provides a 0.3-bits/2D achievable information rate gain over an…

Machine Learning · Computer Science 2025-07-23 Mohammad Taha Askari , Lutz Lampe , Amirhossein Ghazisaeidi

We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D PT -symmetric lattices. For each configuration, we develop a dynamical model and examine its…

Quantum Physics · Physics 2012-10-24 Kai Li , P. G. Kevrekidis , Boris A. Malomed , Uwe Guenther

An optical gateway to convert four-level pulse amplitude modulation to quadrature phase shift keying modulation format having shaping gain was proposed for flexible intensity to phase mapping which exploits non-uniform phase noise. The…

Signal Processing · Electrical Eng. & Systems 2022-04-06 Takahiro Kodama , Toshiaki Koike-Akino , David S. Millar , Keisuke Kojima , Kieran Parsons

We propose two novel techniques to implement sequence selection (SS) for fiber nonlinearity mitigation, demonstrating a nonlinear shaping gain of 0.24 bits/s/Hz, just 0.1 bits/s/Hz below the SS capacity lower bound.

Information Theory · Computer Science 2022-10-25 Stella Civelli , Enrico Forestieri , Marco Secondini

We consider probabilistic shaping to maximize the achievable information rate of coded modulation (CM) with hard decision decoding. The proposed scheme using binary staircase codes outperforms its uniform CM counterpart by more than 1.3 dB…

Information Theory · Computer Science 2017-05-08 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva

A scheme is proposed that combines probabilistic signal shaping with bit-metric decoding. The transmitter generates symbols according to a distribution on the channel input alphabet. The symbols are labeled by bit strings. At the receiver,…

Information Theory · Computer Science 2014-04-22 Georg Böcherer

Probabilistic shaping is a pragmatic approach to improve the performance of coherent optical fiber communication systems. In the nonlinear regime, the advantages offered by probabilistic shaping might increase thanks to the opportunity to…

Information Theory · Computer Science 2024-01-19 Stella Civelli , Enrico Forestieri , Marco Secondini

Quadrature amplitude modulation (QAM), deployed in billions of communication devises, exhibits a shaping-loss of $\pi \mathrm{e}/6$ ($\approx 1.53$ dB) compared to the Shannon-Hartley theorem. With inspiration gained from special (leaf,…

Information Theory · Computer Science 2017-08-25 Peter Larsson

Nonlinear interference models for dual-polarization 4D (DP-4D) modulation have only been used so far to predict signal-signal nonlinear interference. We show that including the signal-noise term in the prediction of the effective…

Signal Processing · Electrical Eng. & Systems 2022-07-18 Zhiwei Liang , Bin Chen , Yi Lei , Gabriele Liga , Alex Alvarado

Achievable information rates (AIRs) of wideband optical communication systems using ~40 nm (~5 THz) EDFA and ~100 nm (~12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each…

Information Theory · Computer Science 2017-03-08 Daniel Semrau , Tianhua Xu , Nikita A. Shevchenko , Milen Paskov , Alex Alvarado , Robert I. Killey , Polina Bayvel

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

Numerical Analysis · Mathematics 2026-01-09 Jiaming Guo , Dunhui Xiao