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

The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fiber 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...

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Bibliographic Details
Published in:IEEE transactions on communications 2018-07, Vol.66 (7), p.2978-2993
Main Authors: Shevchenko, Nikita A., Derevyanko, Stanislav A., Prilepsky, Jaroslaw E., Alvarado, Alex, Bayvel, Polina, Turitsyn, Sergei K.
Format: Article
Language:English
Subjects:
Achievable information rates
Adaptive optics
Amplitude modulation
Amplitudes
channel capacity
Codes
Communication channels
Constellations
Fourier transforms
Gaussian distribution
Integrated optics
Keying
Lower bounds
Mathematical analysis
mutual information
nonlinear Fourier transform
nonlinear optical fibres
Nonlinear optics
Optical fibers
Optical noise
Optical polarization
Optical pulses
optical solitons
Solitary waves
Solitons
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Summary:The channel law for amplitude-modulated solitons transmitted through a nonlinear optical fiber 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 the 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 halfGaussian 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 shiftkeying (ASK) constellations is also numerically analyzed. For the same SNR of 25 dB, a 16-ASK constellation yields a rate of approximately 3.45 bit per channel use.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2018.2808286