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

Hari, Siddarth; Kschischang, Frank R.

doi:10.1109/jlt.2016.2577702

Cited by 43 publications

(40 citation statements)

References 33 publications

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“…A visible effect is the fact that the BER is not the same for the four different constellations, but it is worse for the two constellations associated with the eigenvalue with a higher imaginary part. This effect can be related to the dependency of the noise variance of both the eigenvalues and the corresponding scattering coefficients on the imaginary part of the eigenvalues themselves [44][45][46][47][48]; an analysis of the noise distribution for the various eigenvalues and scattering coefficients is provided in the Supplementary Material. In order to demonstrate fiber transmission with the proposed system, a transmission was performed over a link of N spans of SMF with span length L = 41.5 and L = 83 km.…”

Section: Resultsmentioning

confidence: 99%

Dual-polarization nonlinear Fourier transform-based optical communication system

Gaiarin¹,

Perego²,

Silva³

et al. 2018

Optica

129

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New services and applications are causing an exponential increase in internet traffic. In a few years, current fiber optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Eigenvalue communication could potentially overcome these limitations. It relies on a mathematical technique called "nonlinear Fourier transform (NFT)" to exploit the "hidden" linearity of the nonlinear Schrödinger equation as the master model for signal propagation in an optical fiber. We present here the theoretical tools describing the NFT for the Manakov system and report on experimental transmission results for dual polarization in fiber optic eigenvalue communications. A transmission of up to 373.5 km with bit error rate less than the hard-decision forward error correction threshold has been achieved. Our results demonstrate that dual-polarization NFT can work in practice and enable an increased spectral efficiency in NFT-based communication systems, which are currently based on single polarization channels. OCIS codes:

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Section: Resultsmentioning

confidence: 99%

Dual-polarization nonlinear Fourier transform-based optical communication system

Gaiarin¹,

Perego²,

Silva³

et al. 2018

Optica

129

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“…There are well known problems with the computation of the coefficient b(ζ k ). We used the bi-directional algorithm [17] to find b(ζ k ) by the formula (11). Figure 5 presents the errors (68) of computing the phase coefficients for the maximum eigenvalue ζ 0 (61) with respect to the amplitude A of the potential (59).…”

Section: Numerical Results For Discrete Spectrummentioning

confidence: 99%

Exponential fourth order schemes for direct Zakharov-Shabat problem

et al. 2019

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“…The procedure is a natural generalization of the solitonbased methods [2], the progenitor of NFT-based transmission. The further extension of this direction involves the utilization of norming constants together with eigenvalues [6,14,15,16,17]. Our approach conforms closely with this methodology; the algorithms and signal processing NFT methods developed in our article target fast efficient computation of both the eigenvalues and norming constants.…”

Section: Introductionmentioning

confidence: 91%

“…4.3. However, as we shall see, the computation of the norming constants brings about some additional problems [17,39].…”

Section: Ways Of the Residues Evaluationmentioning

confidence: 99%

Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation

Vasylchenkova

Prilepsky

Shepelsky

et al. 2019

Communications in Nonlinear Science and Numerical Simulation

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Starting from a comparison of some established numerical algorithms for the computation of the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov-Shabat spectral problem, this article delivers new algorithms that combine the best features of the existing ones and thereby allays their relative weaknesses. Our algorithm is modeled within the remit of the so-called direct nonlinear Fourier transform (NFT) associated with the focusing nonlinear Schrödinger equation. First, we present the data for the calibration of existing methods comparing the relative errors associated with the computation of the continuous NF spectrum. Then each method is paired with different numerical algorithms for finding zeros of a complex-valued function to obtain the eigenvalues. Next we describe a new class of methods based on the contour integrals evaluation for the efficient search of eigenvalues. After that we introduce a new hybrid method, one of our main results: the method combines the advances of contour integral approach and makes use of the iterative algorithms at its second stage for the refined eigenvalues search. The veracity of our new hybrid algorithm is established by estimating the convergence speed and accuracy across three independent test profiles. Along with the development of a new approach for the computation of the eigenvalues, our study also addresses the problem of computation of the so-called norming constants associated with the eigenvalues. We show that our formalism effectively amounts to accurate and fast enough computation of residues of the reflection coefficient in the upper complex half-plane of the spectral parameter. ∞ −∞ |q(t, z 0 )| dt < ∞.(2)

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

Cited by 43 publications

References 33 publications

Dual-polarization nonlinear Fourier transform-based optical communication system

Dual-polarization nonlinear Fourier transform-based optical communication system

Exponential fourth order schemes for direct Zakharov-Shabat problem

Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation

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