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Register a new userA Lower Bound on the per Soliton Capacity of the Nonlinear Optical Fibre Channel
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Added by
Nikita A. Shevchenko
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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A closed-form expression for a lower bound on the per soliton capacity of the nonlinear optical fibre channel in the presence of (optical) amplifier spontaneous emission (ASE) noise is derived. This bound is based on a non-Gaussian conditional probability density function for the soliton amplitude jitter induced by the ASE noise and is proven to grow logarithmically as the signal-to-noise ratio increases.
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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.
A correlated phase-and-additive-noise (CPAN) mismatched model is developed for wavelength division multiplexing over optical fiber channels governed by the nonlinear Schrodinger equation. Both the phase and additive noise processes of the CPAN model are Gauss-Markov whereas previous work uses Wiener phase noise and white additive noise. Second order statistics are derived and lower bounds on the capacity are computed by simulations. The CPAN model characterizes nonlinearities better than existing models in the sense that it achieves better information rates. For example, the model gains 0.35 dB in power at the peak data rate when using a single carrier per wavelength. For multiple carriers per wavelength, the model combined with frequency-dependent power allocation gains 0.14 bits/s/Hz in rate and 0.8 dB in power at the peak data rate.
Regular perturbation is applied to the Manakov equation and motivates a generalized correlated phase-and-additive noise model for wavelength-division multiplexing over dual-polarization optical fiber channels. The model includes three hidden Gauss-Markov processes: phase noise, polarization rotation, and additive noise. Particle filtering is used to compute lower bounds on the capacity of multi-carrier communication with frequency-dependent powers and delays. A gain of 0.17 bits/s/Hz/pol in spectral efficiency or 0.8 dB in power efficiency is achieved with respect to existing models at their peak data rate. Frequency-dependent delays also increase the spectral efficiency of single-polarization channels.
We consider the classic joint source-channel coding problem of transmitting a memoryless source over a memoryless channel. The focus of this work is on the long-standing open problem of finding the rate of convergence of the smallest attainable expected distortion to its asymptotic value, as a function of blocklength $n$. Our main result is that in general the convergence rate is not faster than $n^{-1/2}$. In particular, we show that for the problem of transmitting i.i.d uniform bits over a binary symmetric channels with Hamming distortion, the smallest attainable distortion (bit error rate) is at least $Omega(n^{-1/2})$ above the asymptotic value, if the ``bandwidth expansion ratio is above $1$.
A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities, when the ensemble weight spectral shape function tends to a negative value as the fractional codeword weight tends to zero. For these ensembles we can therefore lower bound the block-wise ML decoding threshold. Two examples are presented, namely, linear random parity-check codes and fixed-rate Raptor codes with linear random precoders. While for the former a full analytical solution is possible, for the latter we can lower bound the ML decoding threshold on the erasure channel by simply solving a 2 x 2 system of nonlinear equations.
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