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

Experimental Verification of Rate Flexibility and Probabilistic Shaping by 4D Signaling

The rate flexibility and probabilistic shaping gain of $4$-dimensional signaling is experimentally tested for short-reach, unrepeated transmission. A rate granularity of 0.5 bits/QAM symbol is achieved with a distribution matcher based on a simple look-up table.Comment: Presented at OFC'18, San Diego, CA, US

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog

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

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

Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog