596 research outputs found
Bounds on the Per-Sample Capacity of Zero-Dispersion Simplified Fiber-Optical Channel Models
A number of simplified models, based on perturbation theory, have been
proposed for the fiber-optical channel and have been extensively used in the
literature. Although these models are mainly developed for the low-power
regime, they are used at moderate or high powers as well. It remains unclear to
what extent the capacity of these models is affected by the simplifying
assumptions under which they are derived. In this paper, we consider single
channel data transmission based on three continuous-time optical models i) a
regular perturbative channel, ii) a logarithmic perturbative channel, and iii)
the stochastic nonlinear Schr\"odinger (NLS) channel. We apply two simplifying
assumptions on these channels to obtain analytically tractable discrete-time
models. Namely, we neglect the channel memory (fiber dispersion) and we use a
sampling receiver. These assumptions bring into question the physical relevance
of the models studied in the paper. Therefore, the results should be viewed as
a first step toward analyzing more realistic channels. We investigate the
per-sample capacity of the simplified discrete-time models. Specifically, i) we
establish tight bounds on the capacity of the regular perturbative channel; ii)
we obtain the capacity of the logarithmic perturbative channel; and iii) we
present a novel upper bound on the capacity of the zero-dispersion NLS channel.
Our results illustrate that the capacity of these models departs from each
other at high powers because these models yield different capacity pre-logs.
Since all three models are based on the same physical channel, our results
highlight that care must be exercised in using simplified channel models in the
high-power regime
Conditions for a Monotonic Channel Capacity
Motivated by results in optical communications, where the performance can
degrade dramatically if the transmit power is sufficiently increased, the
channel capacity is characterized for various kinds of memoryless vector
channels. It is proved that for all static point-to-point channels, the channel
capacity is a nondecreasing function of power. As a consequence, maximizing the
mutual information over all input distributions with a certain power is for
such channels equivalent to maximizing it over the larger set of input
distributions with upperbounded power. For interference channels such as
optical wavelength-division multiplexing systems, the primary channel capacity
is always nondecreasing with power if all interferers transmit with identical
distributions as the primary user. Also, if all input distributions in an
interference channel are optimized jointly, then the achievable sum-rate
capacity is again nondecreasing. The results generalizes to the channel
capacity as a function of a wide class of costs, not only power.Comment: This is an updated and expanded version of arXiv:1108.039
Capacity of a Nonlinear Optical Channel with Finite Memory
The channel capacity of a nonlinear, dispersive fiber-optic link is
revisited. To this end, the popular Gaussian noise (GN) model is extended with
a parameter to account for the finite memory of realistic fiber channels. This
finite-memory model is harder to analyze mathematically but, in contrast to
previous models, it is valid also for nonstationary or heavy-tailed input
signals. For uncoded transmission and standard modulation formats, the new
model gives the same results as the regular GN model when the memory of the
channel is about 10 symbols or more. These results confirm previous results
that the GN model is accurate for uncoded transmission. However, when coding is
considered, the results obtained using the finite-memory model are very
different from those obtained by previous models, even when the channel memory
is large. In particular, the peaky behavior of the channel capacity, which has
been reported for numerous nonlinear channel models, appears to be an artifact
of applying models derived for independent input in a coded (i.e., dependent)
scenario
A General Framework for Transmission with Transceiver Distortion and Some Applications
A general theoretical framework is presented for analyzing information
transmission over Gaussian channels with memoryless transceiver distortion,
which encompasses various nonlinear distortion models including transmit-side
clipping, receive-side analog-to-digital conversion, and others. The framework
is based on the so-called generalized mutual information (GMI), and the
analysis in particular benefits from the setup of Gaussian codebook ensemble
and nearest-neighbor decoding, for which it is established that the GMI takes a
general form analogous to the channel capacity of undistorted Gaussian
channels, with a reduced "effective" signal-to-noise ratio (SNR) that depends
on the nominal SNR and the distortion model. When applied to specific
distortion models, an array of results of engineering relevance is obtained.
For channels with transmit-side distortion only, it is shown that a
conventional approach, which treats the distorted signal as the sum of the
original signal part and a uncorrelated distortion part, achieves the GMI. For
channels with output quantization, closed-form expressions are obtained for the
effective SNR and the GMI, and related optimization problems are formulated and
solved for quantizer design. Finally, super-Nyquist sampling is analyzed within
the general framework, and it is shown that sampling beyond the Nyquist rate
increases the GMI for all SNR. For example, with a binary symmetric output
quantization, information rates exceeding one bit per channel use are
achievable by sampling the output at four times the Nyquist rate.Comment: 32 pages (including 4 figures, 5 tables, and auxiliary materials);
submitted to IEEE Transactions on Communication
Demodulation and Detection Schemes for a Memoryless Optical WDM Channel
It is well known that matched filtering and sampling (MFS) demodulation
together with minimum Euclidean distance (MD) detection constitute the optimal
receiver for the additive white Gaussian noise channel. However, for a general
nonlinear transmission medium, MFS does not provide sufficient statistics, and
therefore is suboptimal. Nonetheless, this receiver is widely used in optical
systems, where the Kerr nonlinearity is the dominant impairment at high powers.
In this paper, we consider a suite of receivers for a two-user channel subject
to a type of nonlinear interference that occurs in
wavelength-division-multiplexed channels. The asymptotes of the symbol error
rate (SER) of the considered receivers at high powers are derived or bounded
analytically. Moreover, Monte-Carlo simulations are conducted to evaluate the
SER for all the receivers. Our results show that receivers that are based on
MFS cannot achieve arbitrary low SERs, whereas the SER goes to zero as the
power grows for the optimal receiver. Furthermore, we devise a heuristic
demodulator, which together with the MD detector yields a receiver that is
simpler than the optimal one and can achieve arbitrary low SERs. The SER
performance of the proposed receivers is also evaluated for some single-span
fiber-optical channels via split-step Fourier simulations
Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction
In fiber-optic communications, evaluation of mutual information (MI) is still
an open issue due to the unavailability of an exact and mathematically
tractable channel model. Traditionally, lower bounds on MI are computed by
approximating the (original) channel with an auxiliary forward channel. In this
paper, lower bounds are computed using an auxiliary backward channel, which has
not been previously considered in the context of fiber-optic communications.
Distributions obtained through two variations of the stochastic digital
backpropagation (SDBP) algorithm are used as auxiliary backward channels and
these bounds are compared with bounds obtained through the conventional digital
backpropagation (DBP). Through simulations, higher information rates were
achieved with SDBP, {which can be explained by the ability of SDBP to account
for nonlinear signal--noise interactionsComment: 8 pages, 5 figures, accepted for publication in Journal of Lightwave
Technolog
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