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We show that short-length probabilistic shaping reduces nonlinear interference in optical fiber transmission. SNR improvements of up to 0.8 dB are obtained. The shaping gain vanishes when interleaving is employed and not undone before…

Signal Processing · Electrical Eng. & Systems 2020-03-27 Tobias Fehenberger , Helmut Griesser , Jörg-Peter Elbers

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

In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison…

Information Theory · Computer Science 2020-10-23 Abdelkerim Amari , Lutz Lampe , O. S. Sunish Kumar , Yunus Can Gultekin , Alex Alvarado

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

A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km…

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

Performance trade-offs between linear shaping and nonlinear tolerance of the recently introduced 4D orthant-symmetric 128-ary modulation format are investigated. Numerical simulations show 9.3% reach increase with respect to the 7b4D-2A8PSK…

Information Theory · Computer Science 2020-10-20 Bin Chen , Chigo Okonkwo , Alex Alvarado

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

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

The limited modulation bandwidth of the light emitting diodes (LEDs) presents a challenge in the development of practical high-data-rate visible light communication (VLC) systems. In this paper, a novel adaptive coded probabilistic shaping…

Information Theory · Computer Science 2024-02-22 Amanat Kafizov , Ahmed Elzanaty , Mohamed-Slim Alouini

Probabilistic amplitude shaping (PAS) is a practical means to achieve a shaping gain in optical fiber communication. However, PAS and shaping in general also affect the signal-dependent generation of nonlinear interference. This provides an…

Information Theory · Computer Science 2023-04-18 Mohammad Taha Askari , Lutz Lampe , Jeebak Mitra

We introduce neural probabilistic amplitude shaping, a joint-distribution learning framework for coherent fiber systems. The proposed scheme provides a 0.5 dB signal-to-noise ratio gain over sequence selection for dual-polarized 64-QAM…

Machine Learning · Computer Science 2026-02-04 Mohammad Taha Askari , Lutz Lampe , Amirhossein Ghazisaeidi

Probability Shaping (PS) is a method to improve a Modulation and Coding Scheme (MCS) in order to increase reliability of data transmission. It is already implemented in some modern radio broadcasting and optic systems, but not yet in…

Information Theory · Computer Science 2023-07-06 Evgeny Bobrov , Adyan Dordzhiev

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

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

We report on theoretical and experimental investigations of the nonlinear tolerance of single carrier and digital multicarrier approaches with probabilistically shaped constellations. Experimental transmission of PCS16QAM is assessed at 120…

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 practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly…

Information Theory · Computer Science 2022-06-08 Marco Secondini , Stella Civelli , Enrico Forestieri , Lareb Zar Khan

Probabilistic shaping (PS) has attracted significant attention in intensity-modulation and direct-detection (IM-DD) systems. However, due to the unique system model and inherent constraints, the effective application of the PS technique is…

Signal Processing · Electrical Eng. & Systems 2025-07-25 Dongdong Zou , Wei Wang , Jiawen Yao , Zhongxing Tian , Zeyu Feng , Huan Huang , Fan Li , Gordon Ning Liu , Gangxiang Shen , Yi Cai

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…

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