The performance of optical fiber systems based on nonlinear frequency-division multiplexing (NFDM) or on more conventional transmission techniques is compared through numerical simulations. Some critical issues affecting NFDM systems-namely, the strict requirements needed to avoid burst interaction due to signal dispersion and the unfavorable dependence of performance on burst length-are investigated, highlighting their potentially disruptive effect in terms of spectral efficiency. Two digital processing techniques are finally proposed to halve the guard time between NFDM symbol bursts and reduce the size of the processing window at the receiver, increasing spectral efficiency and reducing computational complexity.

Nonlinear distortion experienced by signals during their propagation through optical fibers strongly limits the throughput of optical communication systems. Recently, a strong research focus has been dedicated to nonlinearity mitigation and compensation techniques. At the same time, a more disruptive approach, the nonlinear Fourier transform (NFT), aims at designing signaling schemes more suited to the nonlinear fiber channel. In a short period, impressive results have been reported by modulating either the continuous spectrum or the discrete spectrum. Additionally, very recent works further introduced the opportunity to modulate both spectra for single polarization transmission. Here, we extend the joint modulation scheme to dual-polarization transmission by introducing the framework to construct a dual-polarization optical signal with the desired continuous and discrete spectra. After a brief analysis of the numerical algorithms used to implement the proposed scheme, the first experimental demonstration of dual-polarization joint nonlinear frequency division multiplexing (NFDM) modulation is reported for up to 3200 km of low-loss transmission fiber. The proposed dual-polarization joint modulation schemes enables to exploit all the degrees of freedom for modulation (both polarizations and both spectra) provided by a single-mode fiber (SMF).

In this work, we study the performance of polarization division multiplexing nonlinear inverse synthesis transmission schemes for fiber-optic communications, expected to have reduced nonlinearity impact. Our technique exploits the integrability of the Manakov equation—the master model for dual-polarization signal propagation in a single mode fiber—and employs nonlinear Fourier transform (NFT) based signal processing. First, we generalize some algorithms for the NFT computation to the two- and multicomponent case. Then, we demonstrate that modulating information on both polarizations doubles the channel information rate with a negligible performance degradation. Moreover, we introduce a novel dual-polarization transmission scheme with reduced complexity which separately processes each polarization component and can also provide a performance improvement in some practical scenarios.

Probabilistic amplitude shaping—implemented through a distribution matcher (DM)—is an effective approach to enhance the performance and the flexibility of bandwidth-efficient coded modulations. Different DM structures have been proposed in the literature. Typically, both their performance and their complexity increase with the block length. In this work, we present a hierarchical DM (Hi-DM) approach based on the combination of several DMs of different possible types, which provides the good performance of long DMs with the low complexity of several short DMs. The DMs are organized in layers. Each upper-layer DM encodes information on a sequence of lower-layer DMs, which are used as “virtual symbols”. First, we describe the Hi-DM structure, its properties, and the encoding and decoding procedures. Then, we present three particular Hi-DM configurations, providing some practical design guidelines, and investigating their performance in terms of rate loss and energy loss. Finally, we compare the system performance obtained with the proposed Hi-DM structures and with their single-layer counterparts: a $0.19\mathrm{d}\mathrm{B}$ SNR gain is obtained by a two-layer Hi-DM based on constant composition DMs (CCDM) compared to a single-layer CCDM with same complexity; a $0.12\mathrm{d}\mathrm{B}$ gain and a significant complexity reduction are obtained by a Hi-DM based on minimum-energy lookup tables compared to a single-layer DM based on enumerative sphere shaping with same memory requirements.

Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result, only little progress has been made so far, while the optimal shaping distribution and the ultimate channel capacity remain unknown. In this work, we describe a novel technique to optimize the shaping distribution in a very general setting and high-dimensional space. For a simplified block-memoryless nonlinear optical channel, the capacity lower bound obtained by the proposed technique can be expressed analytically, establishing the conditions for an unbounded growth of capacity with power. In a more realistic scenario, the technique can be implemented by a rejection sampling algorithm driven by a suitable cost function, and the corresponding achievable information rate estimated numerically. The combination of the proposed technique with an improved (non-Gaussian) decoding metric yields a new capacity lower bound for the dual-polarization WDM channel.

The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( $1\times 180$ km, $15\times 80$ km, and $27\times 80$ km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.