Exponentially-Weighted Energy Dispersion Index for the Nonlinear Interference Analysis of Finite-Blocklength Shaping

A metric called exponentially-weighted energy dispersion index (EEDI) is proposed to explain the blocklength-dependent effective signal-to-noise ratio (SNR) in probabilistically shaped fiber-optic systems. EEDI is better than energy dispersion index (EDI) at capturing the dependency of the effective SNR on the blocklength for long-distance transmission

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

Nonlinearity Tolerant LUT-based Probabilistic Shaping for Extended-Reach Single-Span Links

We propose Huffman-coded sphere shaping (HCSS) as a method for probabilistic constellation shaping which provides improved tolerance to fiber nonlinearities in single-span links. An implementation of this algorithm based on look-up-tables (LUTs) allows for low-complexity, multiplier-free shaping. The advantage of short-length shaping for mitigating fiber nonlinear impairments is experimentally demonstrated for a system employing dual–polarization 64–ary quadrature amplitude modulation (DP-64QAM) at 56 GBd and operating over 210 km of standard single-mode fiber (SSMF). A gain in achievable information rate (AIR) of 0.4 bits/4D-symbol compared with uniform signaling is measured, corresponding to a 100% improvement in shaping gain compared with ideal Maxwell–Boltzmann (MB) shaping. The combinatorial mapping and demapping algorithms can be implemented with integer addition and comparison operations only, utilizing an LUT with 100 kbit size

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