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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,…

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

We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision…

Information Theory · Computer Science 2018-04-04 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva

Probabilistic amplitude shaping (PAS) is a coded modulation strategy in which constellation shaping and channel coding are combined. PAS has attracted considerable attention in both wireless and optical communications. Achievable…

Information Theory · Computer Science 2020-07-14 Yunus Can Gültekin , Alex Alvarado , Frans M. J. Willems

A non-uniform channel input distribution is key for achieving the capacity of arbitrary channels. However, message bits are generally assumed to follow a uniform distribution which must first be transformed to a non-uniform distribution by…

Information Theory · Computer Science 2025-12-19 Frederik Ritter , Andrej Rode , Laurent Schmalen

Probabilistic amplitude shaping (PAS) is on track to become the de facto coded modulation standard for communication systems aiming to operate close to channel capacity at high transmission rates. The essential component of PAS that breeds…

Information Theory · Computer Science 2022-08-16 Yunus Can Gültekin , Frans M. J. Willems , Alex Alvarado

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 present the first neural probabilistic amplitude shaping that outperforms existing methods while accounting for all implementation losses, using a block-less, easily implementable sequential autoregressive encoder compatible with…

Machine Learning · Computer Science 2026-05-28 Mohammad Taha Askari , Lutz Lampe , Amirhossein Ghazisaeidi

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

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

Free-space optical (FSO) transmission enables fast, secure, and efficient next-generation communications with abundant spectrum resources. However, atmospheric turbulence, pointing errors, path loss, and atmospheric loss induce random…

Signal Processing · Electrical Eng. & Systems 2025-11-25 Jingtian Liu , Xiongwei Yang , Yi Wei , Jianjun Yu , Feng Zhao

The interaction between carrier phase recovery and probabilistic amplitude shaping (PAS) in the nonlinear regime is investigated. We show that, for sufficiently high signal-to-noise ratio, the first provides the same inter-channel…

Information Theory · Computer Science 2020-09-03 Stella Civelli , Enrico Forestieri , Marco Secondini

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

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 (PS) has been widely studied and applied to optical fiber communications. The encoder of PS expends the number of bit slots and controls the probability distribution of channel input symbols. Not only studies focused…

Information Theory · Computer Science 2024-01-25 Tsuyoshi Yoshida , Koji Igarashi , Magnus Karlsson , Erik Agrell

We propose a probabilistic shaping approach for region-of-interest signaling, where a low-rate signal controls the desired probabilistic ranges of a high-rate data stream using a flexible distribution controller. In addition, we introduce…

Signal Processing · Electrical Eng. & Systems 2022-09-05 Duc-Phuc Nguyen , Yoshifumi Shiraki , Jun Muramatsu , Takehiro Moriya

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

Integrated sensing and communications (ISAC) promises new use cases for mobile communication systems by reusing the communication signal for radar-like sensing. However, sensing and communications (S&C) impose conflicting requirements on…

Signal Processing · Electrical Eng. & Systems 2026-02-23 Benedikt Geiger , Fan Liu , Shihang Lu , Andrej Rode , Daniel Gil Gaviria , Charlotte Muth , Laurent Schmalen

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

Integrated sensing and communications (ISAC) is considered an innovative technology in sixth-generation (6G) wireless networks, where utilizing orthogonal frequency division multiplexing (OFDM) communication signals for sensing provides a…

Signal Processing · Electrical Eng. & Systems 2025-10-15 Zhen Du , Jingjing Xu , Yifeng Xiong , Jie Wang , Musa Furkan Keskin , Henk Wymeersch , Fan Liu , Shi Jin