41 research outputs found
LDPC Coded Modulation with Probabilistic Shaping for Optical Fiber Systems
An LDPC coded modulation scheme with probabilistic shaping, optimized
interleavers and noniterative demapping is proposed. Full-field simulations
show an increase in transmission distance by 8% compared to uniformly
distributed input.Comment: 3 pages, 3 figures. Paper is accepted for presentation at OFC 2015.
Following the submission to OFC, the blue box in Fig. 1 has been corrected
and reference [3] has been update
On Achievable Rates for Long-Haul Fiber-Optic Communications
Lower bounds on mutual information (MI) of long-haul optical fiber systems
for hard-decision and soft-decision decoding are studied. Ready-to-use
expressions to calculate the MI are presented. Extensive numerical simulations
are used to quantify how changes in the optical transmitter, receiver, and
channel affect the achievable transmission rates of the system. Special
emphasis is put to the use of different quadrature amplitude modulation
formats, channel spacings, digital back-propagation schemes and probabilistic
shaping. The advantages of using MI over the prevailing -factor as a figure
of merit of coded optical systems are also highlighted.Comment: Hard decision mutual information analysis added, two typos correcte
Sensitivity Gains by Mismatched Probabilistic Shaping for Optical Communication Systems
Probabilistic shaping of quadrature amplitude modulation (QAM) is used to
enhance the sensitivity of an optical communication system. Sensitivity gains
of 0.43 dB and 0.8 dB are demonstrated in back-to-back experiments by shaping
of 16QAM and 64QAM, respectively. Further, numerical simulations are used to
prove the robustness of probabilistic shaping to a mismatch between the
constellation used and the signal-to-noise ratio (SNR) of the channel. It is
found that, accepting a 0.1 dB SNR penalty, only four shaping distributions are
required to support these gains for 64QAM.Comment: Title and introduction were updated and the discussion of Section
IV-B was extended. Additionally, some minor modifications were made to the
manuscrip
Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics
The mutual information between a complex-valued channel input and its
complex-valued output is decomposed into four parts based on polar coordinates:
an amplitude term, a phase term, and two mixed terms. Numerical results for the
additive white Gaussian noise (AWGN) channel with various inputs show that, at
high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the
mixed terms. For the AWGN channel with a Gaussian input, analytical expressions
are derived for high SNR. The decomposition method is applied to partially
coherent channels and a property of such channels called "spectral loss" is
developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be
one effect that needs to be taken into account to explain the behavior of the
capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on
Information Theor
Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments
We experimentally investigate mutual information and generalized mutual
information for coherent optical transmission systems. The impact of the
assumed channel distribution on the achievable rate is investigated for
distributions in up to four dimensions. Single channel and wavelength division
multiplexing (WDM) transmission over transmission links with and without inline
dispersion compensation are studied. We show that for conventional WDM systems
without inline dispersion compensation, a circularly symmetric complex Gaussian
distribution is a good approximation of the channel. For other channels, such
as with inline dispersion compensation, this is no longer true and gains in the
achievable information rate are obtained by considering more sophisticated
four-dimensional (4D) distributions. We also show that for nonlinear channels,
gains in the achievable information rate can also be achieved by estimating the
mean values of the received constellation in four dimensions. The highest gain
for such channels is seen for a 4D correlated Gaussian distribution
Four-Dimensional Estimates of Mutual Information in Coherent Optical Communication Experiments
Mutual information is experimentally investigated for long-haul coherent transmission. Receivers that consider memoryless four-dimensional noise distributions can achieve significantly higher rates than receivers assuming two-dimensional symmetric distributions
Successive Interference Cancellation for Bandlimited Channels with Direct Detection
Oversampling increases information rates for bandlimited channels with direct
detection, but joint detection and decoding (JDD) is often too complex to
implement. Two receiver structures are studied to reduce complexity: separate
detection and decoding (SDD) and successive interference cancellation (SIC)
with multi-level coding. For bipolar modulation, frequency-domain raised-cosine
pulse shaping, and fiber-optic channels with chromatic dispersion, SIC achieves
rates close to those of JDD, thereby attaining significant energy gains over
SDD and classic intensity modulation. Gibbs sampling further reduces the
detector complexity and achieves rates close to those of the forward-backward
algorithm at low to intermediate signal-to-noise ratio (SNR) but stalls at high
SNR. Simulations with polar codes and higher-order modulation confirm the
predicted rate and energy gains.Comment: Submitted to IEEE Journal of Lightwave Technology on December 15,
2022; Resubmitted to IEEE Transactions on Communications on September 9,
2023
Experimental Comparison of Probabilistic Shaping Methods for Unrepeated Fiber Transmission
\u3cp\u3eThis paper studies the impact of probabilistic shaping on effective signal-to-noise ratios (SNRs) and achievable information rates (AIRs) in a back-to-back configuration and in unrepeated nonlinear fiber transmissions. For the back-to-back setup, various shaped quadrature amplitude modulation (QAM) distributions are found to have the same implementation penalty as uniform input. By demonstrating in transmission experiments that shaped QAM input leads to lower effective SNR than uniform input at a fixed average launch power, we experimentally confirm that shaping enhances the fiber nonlinearities. However, shaping is ultimately found to increase the AIR, which is the most relevant figure of merit, as it is directly related to spectral efficiency. In a detailed study of these shaping gains for the nonlinear fiber channel, four strategies for optimizing QAM input distributions are evaluated and experimentally compared in wavelength division multiplexing (WDM) systems. The first shaping scheme generates a Maxwell-Boltzmann (MB) distribution based on a linear additive white Gaussian noise channel. The second strategy uses the Blahut-Arimoto algorithm to optimize an unconstrained QAM distribution for a split-step Fourier method based channel model. In the third and fourth approach, MB-shaped QAM and unconstrained QAM are optimized via the enhanced Gaussian noise (EGN) model. Although the absolute shaping gains are found to be relatively small, the relative improvements by EGN-optimized unconstrained distributions over linear AWGN optimized MB distributions are up to 59%. This general behavior is observed in 9-channel and fully loaded WDM experiments.\u3c/p\u3