Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation

Nikita A. Shevchenko, Stanislav A. Derevyanko, Jaroslaw E. Prilepsky, Alex Alvarado, Polina Bayvel, Sergei K. Turitsyn

Research output: Contribution to journalArticle

Abstract

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with 2n degrees of freedom, where n = 2 and n = 3 correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary n and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of n. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for n = 1; 2; 3. At an SNR of 25 dB, the best lower bounds we developed are approximately 3:68 bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of 25 dB, a 16- ASK constellation yields a rate of approximately 3:45 bit per channel use.
Original languageEnglish
Pages (from-to)1-1
JournalIEEE Transactions on Communications
DOIs
Publication statusPublished - 20 Feb 2018

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Amplitude modulation
Solitons
Signal to noise ratio
Amplification
Optical fibers
Fourier transforms
Polarization
Amplitude shift keying

Bibliographical note

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Funding: Engineering and Physical Sciences Research Council (EPSRC) project UNLOC (EP/J017582/1), by the Netherlands Organisation
for Scientific Research (NWO) via the VIDI Grant ICONIC (project
number 15685), and a UCL Graduate Research Scholarship (GRS).

Keywords

  • Core losses, mutual inductance, stator windings, switched reluctance machine (SRM), torque ripple

Cite this

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Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation. / Shevchenko, Nikita A.; Derevyanko, Stanislav A.; Prilepsky, Jaroslaw E.; Alvarado, Alex; Bayvel, Polina; Turitsyn, Sergei K.

In: IEEE Transactions on Communications, 20.02.2018, p. 1-1.

Research output: Contribution to journalArticle

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T1 - Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation

AU - Shevchenko, Nikita A.

AU - Derevyanko, Stanislav A.

AU - Prilepsky, Jaroslaw E.

AU - Alvarado, Alex

AU - Bayvel, Polina

AU - Turitsyn, Sergei K.

N1 - © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. Funding: Engineering and Physical Sciences Research Council (EPSRC) project UNLOC (EP/J017582/1), by the Netherlands Organisation for Scientific Research (NWO) via the VIDI Grant ICONIC (project number 15685), and a UCL Graduate Research Scholarship (GRS).

PY - 2018/2/20

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N2 - The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fibre with ideal distributed amplification and a receiver based on the nonlinear Fourier transform is a noncentral chi-distribution with 2n degrees of freedom, where n = 2 and n = 3 correspond to the single- and dual-polarisation cases, respectively. In this paper, we study capacity lower bounds of this channel under an average power constraint in bits per channel use. We develop an asymptotic semi-analytic approximation for a capacity lower bound for arbitrary n and a Rayleigh input distribution. It is shown that this lower bound grows logarithmically with signal-to-noise ratio (SNR), independently of the value of n. Numerical results for other continuous input distributions are also provided. A half-Gaussian input distribution is shown to give larger rates than a Rayleigh input distribution for n = 1; 2; 3. At an SNR of 25 dB, the best lower bounds we developed are approximately 3:68 bit per channel use. The practically relevant case of amplitude shift-keying (ASK) constellations is also numerically analysed. For the same SNR of 25 dB, a 16- ASK constellation yields a rate of approximately 3:45 bit per channel use.

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KW - Core losses, mutual inductance, stator windings, switched reluctance machine (SRM), torque ripple

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JF - IEEE Transactions on Communications

SN - 0090-6778

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