Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

J.E. Prilepsky, S.A. Derevyanko, S.K. Turitsyn

Research output: Contribution to conferenceAbstract

Abstract

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse
scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9].
REFERENCES
1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972.
2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993.
3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014.
4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014.
5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014.
6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014.
7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014.
8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978.
9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.
Original languageEnglish
Pages492
Number of pages1
Publication statusPublished - 2015
EventProgress in Electromagnetics Research Symposium - Prague, Czech Republic
Duration: 6 Jul 20156 Jul 2015

Symposium

SymposiumProgress in Electromagnetics Research Symposium
Abbreviated titlePIERS 2015 Prague
CountryCzech Republic
CityPrague
Period6/07/156/07/15

Fingerprint

nonlinear equations
white noise
communication
channel noise
impairment
inverse scattering
spontaneous emission
autocorrelation
emerging
eigenvalues
perturbation theory
modulation
symmetry
synthesis

Bibliographical note

Invited.
Progress in Electromagnetics Research Symposium Abstracts

Cite this

Prilepsky, J. E., Derevyanko, S. A., & Turitsyn, S. K. (2015). Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform. 492. Abstract from Progress in Electromagnetics Research Symposium, Prague, Czech Republic.
Prilepsky, J.E. ; Derevyanko, S.A. ; Turitsyn, S.K. / Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform. Abstract from Progress in Electromagnetics Research Symposium, Prague, Czech Republic.1 p.
@conference{ae0f88c613954993b843911fc62228d7,
title = "Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform",
abstract = "The integrability of the nonlinear Schr{\"a}odinger equation (NLSE) by the inversescattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring{"}, its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies{"}, and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9].REFERENCES1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972.2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993.3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014.4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014.5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014.6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014.7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014.8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978.9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.",
author = "J.E. Prilepsky and S.A. Derevyanko and S.K. Turitsyn",
note = "Invited. Progress in Electromagnetics Research Symposium Abstracts; Progress in Electromagnetics Research Symposium, PIERS 2015 Prague ; Conference date: 06-07-2015 Through 06-07-2015",
year = "2015",
language = "English",
pages = "492",

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Prilepsky, JE, Derevyanko, SA & Turitsyn, SK 2015, 'Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform' Progress in Electromagnetics Research Symposium, Prague, Czech Republic, 6/07/15 - 6/07/15, pp. 492.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform. / Prilepsky, J.E.; Derevyanko, S.A.; Turitsyn, S.K.

2015. 492 Abstract from Progress in Electromagnetics Research Symposium, Prague, Czech Republic.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

AU - Prilepsky, J.E.

AU - Derevyanko, S.A.

AU - Turitsyn, S.K.

N1 - Invited. Progress in Electromagnetics Research Symposium Abstracts

PY - 2015

Y1 - 2015

N2 - The integrability of the nonlinear Schräodinger equation (NLSE) by the inversescattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9].REFERENCES1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972.2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993.3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014.4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014.5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014.6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014.7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014.8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978.9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

AB - The integrability of the nonlinear Schräodinger equation (NLSE) by the inversescattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9].REFERENCES1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972.2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993.3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014.4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014.5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014.6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014.7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014.8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978.9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

M3 - Abstract

SP - 492

ER -

Prilepsky JE, Derevyanko SA, Turitsyn SK. Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform. 2015. Abstract from Progress in Electromagnetics Research Symposium, Prague, Czech Republic.