Multieigenvalue communication paired with b-modulation

Vasylchenkova, Anastasiia; Prylepsky, J.E.; Chichkov, Nikolai B.; Turitsyn, Sergei K.

doi:10.1049/cp.2019.0942

Cited by 6 publications

(7 citation statements)

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“…The arguments of Portinari were recently carried over the NLS case in [19], where the characterisation problem has also been addressed in the presence of eigenvalues, by exploiting the spectral properties of one-sided signals. At this place we would like to emphasize that the recent works [21], [22] propose to put an arbitrary not provide truly localised signals, and in our current study, we require a strict localisation of the time-domain signal, similarly to the initial definition of b-modulation [8]. Finally, we note that the results of Brenne and Skaar in [23] can be viewed as the discrete-time analogue of the results given in our paper.…”

mentioning

confidence: 68%

Nonlinear Fourier Spectrum Characterization of Time-Limited Signals

Shepelsky

Vasylchenkova

Prilepsky

et al. 2020

IEEE Trans. Commun.

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Addressing the optical communication systems employing the nonlinear Fourier transform (NFT) for the data modulation/demodulation, we provide an explicit proof for the properties of the signals emerging in the so-called b-modulation method, the nonlinear signal modulation technique that provides explicit control over the signal extent. We present details of the procedure and related rigorous mathematical proofs addressing the case where the time-domain profile corresponding to the b-modulated data has a limited duration, and when the bound states corresponding to specifically chosen discrete solitonic eigenvalues and norming constants, are also present. We also prove that the number of solitary modes that we can embed without violating the exact localisation of the time-domain profile, is actually infinite. Our theoretical findings are illustrated with numerical examples, where simple example waveforms are used for the b-coefficient, demonstrating the validity of the developed approach. We also demonstrate the influence of the bound states on the noise tolerance of the b-modulated system.

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mentioning

confidence: 68%

Nonlinear Fourier Spectrum Characterization of Time-Limited Signals

Shepelsky

Vasylchenkova

Prilepsky

et al. 2020

IEEE Trans. Commun.

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“…3 to create nonlinear extensions to n A and n φ . Using the nonlinearly extended vectors n A,NL and n φ,NL in conjunction with (20), (21) c NL and d NL can be calculated, which can be used for nonlinear equalization. The amount of total coefficents to be computed for each n NL can be calculated using…”

Section: Nonlinear Equalizermentioning

confidence: 99%

“…To further optimize the transmission performance, several techniques have been proposed and experimentally verified. It has been shown, that detecting only the b-coefficient for data modulation can increase the performance [18]- [21]. Furthermore, it has been observed, that using eigenvalues with realparts leads to a position shift of the time domain signal in the symbol period while propagating in the fiber, which can be compensated by pre-shifting the soliton at the transmitter site [19].…”

Section: Introductionmentioning

confidence: 99%

Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

Koch

Chan

Schaeffer

et al. 2021

IEEE J. Select. Topics Quantum Electron.

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A minimum mean squared error (MMSE) equalizer is a way to effectively increase transmission performance for nonlinear Fourier transform (NFT) based communication systems. Other equalization schemes, based on nonlinear equalizer approaches or neural networks, are interesting for NFT transmission due to their ability to deal with nonlinear correlations of the NFTs' eigenvalues and their coefficients. We experimentally investigated single-and dual-polarization long haul transmission with several modulation schemes and compared different equalization techniques including joint detection equalization and the use of neural networks. We observed that joint detection equalization provides range increases for shorter transmission distances while having low numeric complexity. We could further achieve bit error rates (BER) under HD-FEC for significant longer transmission distances in comparison to no equalization with different equalizers.

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“…(Note that functions in PW 1 σ are entire and therefore already uniquely specified their values on the real line.) Theorem 6 in [18] ensures that for any b(z 0 , •) ∈ PW 1 2T with |b(z 0 , ξ)| < 1 for all ξ ∈ R, and any discrete spectrum (λ n , b n ) that satisfies (7), there is exactly one signal q(z 0 , •) ∈ L 1 with this nonlinear spectrum. This signal satisfies (5).…”

Section: Nonlinear Fourier Transform Of Time-limited Signalsmentioning

confidence: 99%