Introducing 4D Geometric Shell Shaping for Mitigating Nonlinear Interference Noise

Goossens, Sebastiaan; Gültekin, Yunus Can; Vassilieva, Olga; Kim, Inwoong; Palacharla, Paparao; Okonkwo, Chigo; Alvarado, Alex

doi:10.1109/jlt.2022.3220402

Cited by 16 publications

(15 citation statements)

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“…At the receiver, AWGN is added to the fiber output to emulate the shot noise from the coherent receiver. Similar to [44], we consider a coherent receiver with a minimum sensitivity of −20 dBm, and the amount of noise that is added to the fiber output signal is −33.5 dBm. In a backto-back setup, such a configuration will allow for achieving a pre-FEC bit error rate (BER) of 1.25 • 10 −2 , which is the maximum BER that can be tolerated by the FEC block in the 400ZR standard [45] to fulfill the post decoding error rate requirements.…”

Section: A Nonlinear Optical Fiber Channelmentioning

confidence: 99%

Blind Channel Equalization Using Vector-Quantized Variational Autoencoders

Song¹,

Lauinger²,

Wu³

et al. 2023

Preprint

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State-of-the-art high-spectral-efficiency communication systems employ high-order modulation formats coupled with high symbol rates to accommodate the ever-growing demand for data rate-hungry applications. However, such systems are more vulnerable to linear and nonlinear transmission impairments, and it is important to mitigate the performance loss via digital signal processing. In this paper, we propose a novel machine learning approach for blind channel equalization and estimation using the vector quantized (VQ) variational autoencoder (VAE) framework. The proposed approach generalizes the applicability of the conventional VAE-based equalizer to nonlinear systems employing high-order modulation formats by introducing a codebook component and an associated novel loss function. We evaluate the performance of the proposed method over a linear additive white Gaussian noise channel with intersymbol interference and two nonlinear scenarios. Simulation results show that the proposed method can achieve similar performance as a data aided equalizer using the minimum-mean-squarederror (MMSE) criterion, and outperforms the blind constant modulus algorithm (CMA) and the VAE-based channel equalizer. Furthermore, we show that for the linear channel, the proposed scheme exhibits better convergence properties than the MMSEbased, the CMA-based, and the VAE-based equalizers in terms of both convergence speed and robustness to variations in training batch size and learning rate. I. INTRODUCTIONThe performance of communication systems is constrained by the linear and nonlinear distortions originating from hardware impairments and non-ideal communication channels.

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Section: A Nonlinear Optical Fiber Channelmentioning

confidence: 99%

Blind Channel Equalization Using Vector-Quantized Variational Autoencoders

Song¹,

Lauinger²,

Wu³

et al. 2023

Preprint

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“…In order to harvest most of the gains in the nonlinear fiber channel, heuristic ideas have been used in the literature. These include for example adding constraints of constant modulus [11], [12] and shell shaping [7] in the optimization. Such heuristics have the potential to significantly reduce the NLI, however, to fully maximize the performance in the nonlinear channel, an accurate NLI modelling is required.…”

Section: Introductionmentioning

confidence: 99%

Analytical Model of Nonlinear Fiber Propagation for General Dual-Polarization Four-Dimensional Modulation Format

Liang¹,

Chen²,

Long³

et al. 2023

Preprint

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Coherent dual-polarization (DP) optical transmission systems encode information on the four available degrees of freedom of an optical field: the two polarization states, each with two quadrature components. Such systems naturally operate based on a four-dimensional (4D) signal space. Having a general analytical model to accurately estimate nonlinear interference (NLI) is key to analyze such transmission systems as well as to study how different DP-4D formats are affected by NLI. However, the available models in the literature are not completely general. They either do not apply to the entire DP-4D formats or do not consider all the NLI contributions. In this paper we develop a model that applies to the entire class of DP-4D modulation formats. Our model takes self-channel interference, crosschannel interference and multiple-channel interference effects into account. As an application of our model, we further study the effects of signal-noise interactions in long-haul transmission via the proposed model. When compared to previous results in the literature, our model is more accurate at predicting the contribution of NLI for both low and high dispersion fibers in single-and multi-channel transmission systems. For the NLI, we report an average gap from split step Fourier simulation results below 0.15 dB. The simulation results further show that by considering signal-noise interactions, the proposed model in longhaul transmission improves the NLI power accuracy prediction by up to 8.5%.

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“…3,4 The commonly used constellation shaping techniques include probabilistic shaping (PS) and geometric shaping (GS). 5,6 The constellation points of GS are equiprobable. The shaping gain of GS was obtained by optimizing the distribution of constellation points with criteria that include minimizing the bit error rate (BER) and maximizing the mutual information (MI).…”

Section: Introductionmentioning

confidence: 99%

“…The commonly used constellation shaping techniques include probabilistic shaping (PS) and geometric shaping (GS) 5 , 6 . The constellation points of GS are equiprobable.…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of hybrid geometric-probabilistic shaped 8/12 quadrature amplitude modulation for coherent optical communication system

Liu

et al. 2023

Opt. Eng.

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.A hybrid shaping (HS) scheme based on geometric shaping (GS) and probabilistic shaping (PS) in a coherent optical communication system is proposed. A particle swarm optimization algorithm and Maxwell-Boltzmann distribution are employed to sequentially implement GS and PS. The results demonstrate that hybrid shaped 8/12-ary quadrature amplitude modulation (HS-8/12QAM) is superior to regular-8/12QAM (R-8/12QAM) in terms of reducing the bit error rate (BER) and increasing the generalized mutual information (GMI). HS-8QAM achieves a 2 dB optical signal-to-noise ratio (OSNR) gain and 0.45 bits / symbol GMI gain compared with R-8QAM. Meanwhile, HS-12QAM achieves 1.9 dB OSNR gain and 0.68 bits/symbol GMI gain compared with R-12QAM. In addition, HS-8/12QAM is better than R-8/12QAM in terms of transmission distance and data rate.

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Introducing 4D Geometric Shell Shaping for Mitigating Nonlinear Interference Noise

Cited by 16 publications

References 50 publications

Blind Channel Equalization Using Vector-Quantized Variational Autoencoders

Blind Channel Equalization Using Vector-Quantized Variational Autoencoders

Analytical Model of Nonlinear Fiber Propagation for General Dual-Polarization Four-Dimensional Modulation Format

Performance analysis of hybrid geometric-probabilistic shaped 8/12 quadrature amplitude modulation for coherent optical communication system

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