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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,…

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

We review the design of multidimensional modulations by maximizing generalized mutual information and compare the maximum transmission reach of recently introduced 4D formats. A model-based optimization for nonlinear-tolerant 4D modulations…

Signal Processing · Electrical Eng. & Systems 2021-12-24 Bin Chen , Gabriele Liga , Yi Lei , Wei Ling , Zhengyan Huan , Xuwei Xue , Alex Alvarado

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…

The performance of different probabilistic amplitude shaping (PAS) techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS…

Information Theory · Computer Science 2023-05-24 Stella Civelli , Emanuele Parente , Enrico Forestieri , Marco Secondini

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 propose two 8-dimensional (8D) modulation formats (8D-2048PRS-T1 and 8D-2048PRS-T2) with a spectral efficiency of 5.5 bit/4D-sym, where the 8 dimensions are obtained from two time slots and two polarizations. Both formats provide a…

Signal Processing · Electrical Eng. & Systems 2019-09-30 Bin Chen , Chigo Okonkwo , Hartmut Hafermann , Alex Alvarado

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

We demonstrate a polarization-managed 8-dimensional modulation format that is time domain coded to reduce inter-channel nonlinearity. Simulation results show a 2.33 dB improvement in maximum net system margin (NSM) relative to polarization…

The novel 3-dimensional modulation format 3D-Simplex offers potentially 1.2 dB higher OSNR tolerance than DP-DPSK while exhibiting the same spectral occupancy, modulating two bits per symbol. We verify this benefit experimen-tally and…

Signal Processing · Electrical Eng. & Systems 2020-09-22 Annika Dochhan , Helmut Grießer , Brian Teipen , Michael Eiselt

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

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…

We numerically and experimentally investigate the laser phase noise tolerance of probabilistically shaped (PS) and uniformly shaped (US) quadrature amplitude modulation (QAM) signals. In the simulations, we compare PS-64QAM to US-16QAM,…

Signal Processing · Electrical Eng. & Systems 2020-12-16 Takeo Sasai , Asuka Matsushita , Masanori Nakamura , Seiji Okamoto , Fukutaro Hamaoka , Yoshiaki Kisaka

By tailoring probabilistic constellation shaping (PCS) for nonlinearity tolerance, we experimentally demonstrate up to 1.1 dB increase in signal-to-noise ratio (SNR) and 6.4% increase in total net data rate (NDR) compared to…

Signal Processing · Electrical Eng. & Systems 2020-12-10 Junho Cho , Xi Chen , Greg Raybon , Di Che , Ellsworth Burrows , Robert Tkach

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

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

The four-dimensional nonlinear model is extended to include the inter-channel stimulated Raman scattering, enabling accurate prediction of dual-polarization four-dimensional modulation formats and probabilistically shaped constellations in…

Signal Processing · Electrical Eng. & Systems 2025-09-15 Zhiwei Liang , Bin Chen , Jiwei Xu , Yi Lei , Qingqing Hu , Fan Zhang , Gabriele Liga

We experimentally demonstrate a novel 3-dimensional modulation format with 1.2-dB OSNR tolerance improvement potential compared to DP-BPSK, as verified for the linear case. The non-linearity tolerance is evaluated in single-span…

Signal Processing · Electrical Eng. & Systems 2020-05-12 Annika Dochhan , Helmut Griesser , Michael Eiselt

In this paper, the quasi-constant modulus (QCM) property is analyzed and leveraged in the design of nonlinearity-tolerant four-dimensional (4D) modulation formats. Accordingly, we propose a family of QCM-based quadrature amplitude…

Signal Processing · Electrical Eng. & Systems 2026-04-21 Junzhe Xiao , Zekun Niu , Lyu Li , Minghui Shi , Weisheng Hu , Lilin Yi

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…

Signal Processing · Electrical Eng. & Systems 2024-01-25 Ali Mirani , Erik Agrell , Magnus Karlsson