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

doi:10.1109/TCOMM.2018.2808286

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 journal › Article › peer-review

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 language	English
Pages (from-to)	2978 - 2993
Number of pages	16
Journal	IEEE Transactions on Communications
Volume	66
Issue number	7
Early online date	20 Feb 2018
DOIs	https://doi.org/10.1109/TCOMM.2018.2808286
Publication status	Published - 1 Jul 2018

Bibliographical note

This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/

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
torque ripple
switched reluctance machine (SRM)
stator windings

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

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title = "Capacity Lower Bounds of the Noncentral Chi-Channel with Applications to Soliton Amplitude Modulation",

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.",

keywords = "Core losses, mutual inductance, torque ripple, switched reluctance machine (SRM), stator windings",

author = "Shevchenko, {Nikita A.} and Derevyanko, {Stanislav A.} and Prilepsky, {Jaroslaw E.} and Alex Alvarado and Polina Bayvel and Turitsyn, {Sergei K.}",

note = "This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ 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). ",

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AU - Prilepsky, Jaroslaw E.

AU - Alvarado, Alex

AU - Bayvel, Polina

AU - Turitsyn, Sergei K.

N1 - This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ 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).

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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.

AB - 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.

KW - Core losses

KW - mutual inductance

KW - torque ripple

KW - switched reluctance machine (SRM)

KW - stator windings

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JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

IS - 7

ER -

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

Abstract

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Keywords

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A Lower Bound on the Capacity of the Noncentral Chi Channel with Applications to Soliton Amplitude Modulation

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

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A Lower Bound on the Capacity of the Noncentral Chi Channel with Applications to Soliton Amplitude Modulation

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