Numerical methods for the inverse nonlinear fourier transform

Civelli, Stella; Barletti, Luigi; Secondini, Marco

doi:10.1109/tiwdc.2015.7323325

Cited by 14 publications

(22 citation statements)

References 12 publications

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“…As noted in [66], the NFT shares many of the properties of the ordinary Fourier transform, including the generalized Parseval identity Despite their apparent promise at achieving relatively large spectral efficiencies and enabling transmission at higher launch powers than conventional techniques, considerably more work needs to be done before any of these NFT-based techniques will be competitive in practice. The computational resources required to compute forward and inverse NFTs numerically, even using the fast algorithms of [82][83][84], is substantial. The impact on the overall transmission system of larger launch powers and nonstandard waveforms needs to be assessed.…”

Section: Probabilistic Shapingmentioning

confidence: 99%

Digital signal processing for fiber nonlinearities [Invited]

Cartledge¹,

Guiomar²,

Kschischang³

et al. 2017

Opt. Express

145

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This paper reviews digital signal processing techniques that compensate, mitigate, and exploit fiber nonlinearities in coherent optical fiber transmission systems. References and links1. A. Mecozzi and R.-J. Essiambre, "Nonlinear Shannon limit in pseudolinear coherent systems," J. Lightw. Technol. 2011-2024 (2012). 2. A. Mecozzi, C. B. Clausen, and M. Shtaif, "Analysis of intrachannel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12(4), 392-394 (2000). 3. L. Dou, Z. Tao, L. Li, W. Yan, T. Tanimura, T. Hoshida, and J. C. Rasmussen, "A low complexity pre-distortion method for intra-channel nonlinearity," in Optical Fiber Communication Conference (2011), paper OThF5. 4. Z. Tao, L. Dou, W. Yan, L. Li, T. Hoshida, and J. C. Rasmussen, "Multiplier-free intrachannel nonlinearity compensating algorithm operating at symbol rate," J. Lightw. Technol. 29(17), 2570-2576 (2011). 5. T. Oyama, H. Nakashima, S. Oda, T. Yamauchi, Z. Tao, T. Hoshida, and J. C. Rasmussen, "Robust and efficient receiver-side compensation method for intra-channel nonlinear effects," in Optical Fiber Communication Conference (2014), paper Tu3A.3. 6. A. Ghazisaeidi, I. Fernandez de Jauregui Ruiz, L. Schmalen, P. Tran, P. Brindel, C. Simonneau, E. Awwad, B. 30(12),Uscumlic, P. Brindel, and G. Charlet, "Submarine transmission systems using digital nonlinear compensation and adaptive rate forward error correction," IEEE/OSA J. Lightw. Technol. 34(8), 1886-1895 (2016 Vol. 25, No. 3 | 6 Feb 2017 | OPTICS EXPRESS 1918 eigenvalue division multiplexing in optical fiber channels," Phys. Rev. Lett. 113(1), 013901 (2014

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Section: Probabilistic Shapingmentioning

confidence: 99%

Digital signal processing for fiber nonlinearities [Invited]

Cartledge¹,

Guiomar²,

Kschischang³

et al. 2017

Opt. Express

145

View full text Add to dashboard Cite

show abstract

“…There has been a lot of recent work on the NFT [1]- [8], including experimental demonstration of NFT-based transmission strategies [9]- [15] and numerical methods [16]- [18] focused on "fast" algorithms. A final branch of research has been the information-theoretical understanding of the optical channel in the NFT-spectral domain, including noise models [19], [20] and bounds on "per-soliton" capacity [21].…”

Section: Introductionmentioning

confidence: 99%

Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT

Hari

Kschischang

2016

J. Lightwave Technol.

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The nonlinear Fourier transform (NFT) represents a signal in terms of its continuous spectrum, discrete eigenvalues and the corresponding discrete spectral amplitudes. This paper presents a new bi-directional algorithm for computing the discrete spectral amplitudes, which addresses the significant problem of rounding errors inherent in previously-known techniques. We use the proposed method to obtain accurate spectral-domain noise statistics for 2-soliton signals using numerical simulation.

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“…At the end we mention a recent work on the INFT methods by Civelli et al [129]: the authors introduced yet another INFT first order solution algorithm based on iterated convolutions with the GLME kernel using the FFT, which demonstrated the better performance in terms of accuracy and time consumption that the 1st order TIB [52] and the Nyström conjugate gradient method [130]. However, the last approach has not been tested so far on the transmission-related problems.…”

Section: B Numerical Methods For the Inftmentioning

confidence: 99%

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

Turitsyn

Prilepsky

et al. 2017

Optica

315

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Fiber-optic communication systems are nowadays facing serious challenges due to fast growing demand on capacity from various new applications and services. It is now well recognised that nonlinear effects limit the spectral efficiency and transmission reach of modern fiber-optic communications. Nonlinearity compensation is therefore widely believed to be of paramount importance for increasing the capacity of future optical networks. Recently, there has been a steadily growing interest in the application of a powerful mathematical tool -the nonlinear Fourier transform (NFT) -in the development of fundamentally novel nonlinearity mitigation tools for fiber-optic channels. It has been recognized that, within this paradigm, the nonlinear crosstalk due to the Kerr effect is effectively absent, and fiber nonlinearity due to Kerr effect can enter as a constructive element rather than a degrading factor. The novelty and the mathematical complexity of the NFT, the versatility of the proposed system designs, and the lack of a unified vision of an optimal NFT-type communication system however constitute significant difficulties for communication researchers. In this paper, we therefore survey the existing approaches in a common framework and review the progress in this area with a focus on practical implementation aspects. First, an overview of existing key algorithms for the efficacious computation of the direct and inverse NFT is given, and the issues of accuracy and numerical complexity are elucidated. We then describe different approaches for the utilization of the NFT in practical transmission schemes. After that we discuss the differences, advantages and challenges of various recently emerged system designs employing the NFT, and the efficiency estimation available up-to-date. With many practical implementation aspects still being open, our minireview is aimed at helping researchers to assess the perspectives, understand the bottle-necks, and envision the development paths in the upcoming of NFT-based transmission technologies.

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Numerical methods for the inverse nonlinear fourier transform

Abstract: We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the proposed method requires the lowest number of operations

Cited by 14 publications

References 12 publications

Digital signal processing for fiber nonlinearities [Invited]

Digital signal processing for fiber nonlinearities [Invited]

Bi-Directional Algorithm for Computing Discrete Spectral Amplitudes in the NFT

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

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