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Probabilistic shaping of quadrature amplitude modulation (QAM) is used to enhance the sensitivity of an optical communication system. Sensitivity gains of 0.43 dB and 0.8 dB are demonstrated in back-to-back experiments by shaping of 16QAM…

Information Theory · Computer Science 2016-01-19 Tobias Fehenberger , Domaniç Lavery , Robert Maher , Alex Alvarado , Polina Bayvel , Norbert Hanik

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

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…

Different aspects of probabilistic shaping for a multi-span optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input…

Information Theory · Computer Science 2016-07-29 Tobias Fehenberger , Alex Alvarado , Georg Böcherer , Norbert Hanik

Probabilistic constellation shaping has been used in long-haul optically amplified coherent systems for its capability to approach the Shannon limit and realize fine rate granularity. The availability of high-bandwidth optical-electronic…

Signal Processing · Electrical Eng. & Systems 2023-03-31 Md Sabbir-Bin Hossain , Georg Bocherer , Talha Rahman , Tom Wettlin , Nebojsa Stojanovic , Stefano Calabro , Stephan Pachnicke

We implemented a flexible transmission system operating at adjustable data rate and fixed bandwidth, baudrate, constellation and overhead using probabilistic shaping. We demonstrated in a transmission experiment up to 15% capacity and 43%…

Information Theory · Computer Science 2015-09-30 Fred Buchali , Georg Böcherer , Wilfried Idler , Laurent Schmalen , Patrick Schulte , Fabian Steiner

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

This paper studies the impact of probabilistic shaping on effective signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a back-to-back configuration and in unrepeated nonlinear fiber transmissions. For back-to-back,…

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

The rate flexibility and probabilistic shaping gain of $4$-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a…

A class of circular 64-QAM that combines 'geometric' and 'probabilistic' shaping aspects is presented. It is compared to square 64-QAM in back-to-back, single-channel, and WDM transmission experiments. First, for the linear AWGN channel…

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

Integrated sensing and communications is regarded as a key enabling technology in the sixth generation networks, where a unified waveform, such as orthogonal frequency division multiplexing (OFDM) signal, is adopted to facilitate both…

Signal Processing · Electrical Eng. & Systems 2023-12-27 Zhen Du , Fan Liu , Yifeng Xiong , Tony Xiao Han , Yonina C. Eldar , Shi Jin

Probabilistic shaping for intensity modulation and direct detection (IM/DD) links is discussed and a peak power constraint determined by the limited modulation extinction ratio (ER) of optical modulators is introduced. The input…

Information Theory · Computer Science 2021-02-03 Thomas Wiegart , Francesco Da Ros , Metodi Plamenov Yankov , Fabian Steiner , Simone Gaiarin , Richard Wesel

Optical orthogonal frequency-division multiplexing (OFDM) and probabilistic constellation shaping (PCS) have emerged as powerful techniques to enhance the performance of optical wireless communications (OWC) systems. While PCS improves…

Systems and Control · Electrical Eng. & Systems 2025-07-11 Thanh V. Pham , Susumu Ishihara

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 wireless communication systems, there are many stages for signal transmission. Among them, mapping and demapping convert a sequence of bits into a sequence of complex numbers and vice versa. This operation is performed by a system of…

Information Theory · Computer Science 2023-03-07 Daniil Yudakov , Dmitrii Kolosov , Evgeny Bobrov

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

An end-to-end learning method for constellation shaping with a shaping-encoder assisted transceiver architecture is presented. The shaping encoder, which produces shaping bits with a higher probability of zeros, is used to produce an…

Information Theory · Computer Science 2025-10-28 Harindu Jayarathne , Dileepa Marasinghe , Nandana Rajatheva , Matti Latva-aho
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