Probabilistic shaping is a pragmatic approach to improve the performance of coherent optical fiber communication systems. In the nonlinear regime, the advantages offered by probabilistic shaping might increase thanks to the opportunity to obtain an additional nonlinear shaping gain. Unfortunately, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in scenarios of limited practical interest. In this manuscript we use sequence selection to investigate the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 bit/s/Hz gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols: they must be known to compute the selection metric, but there is no need to shape them. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if these are modified. Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC) and complexity. Overall, the single block and the multi block FEC-independent bit scrambling are the best options, with a gain up to 0.08 bit/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included.

翻译：概率整形是一种提升相干光纤通信系统性能的实用方法。在非线性区域，由于可能获得额外的非线性整形增益，概率整形带来的优势或许会进一步增加。然而，对传统整形技术（如概率幅度整形，PAS）的优化仅在实用价值有限的情形下才能产生可观的非线性整形增益。本文利用序列选择来探究概率整形在非线性信道中的潜力、机遇与挑战。首先，我们表明，与具有优化块长度的PAS相比，理想序列选择能够提供高达0.13比特/秒/赫兹的增益。然而，只有在选择度量考虑符号的极性时才能获得这一额外增益：计算选择度量需要知晓这些极性，但无需对其进行整形。此外，我们指出，序列选择对符号速率和链路长度的依赖性并不关键：针对特定场景选择的序列在这些参数改变时仍能提供可观的增益。接着，我们考虑与前向纠错（FEC）的交互及复杂度，分析并比较了序列选择的几种实际实现方案。总体而言，单块和多块独立于FEC的比特随机化是最优选择，可带来高达0.08比特/秒/赫兹的增益。其实际实现的主要挑战和限制仍在于度量的评估，当前复杂度过高。最后，我们证明，在包含载波相位恢复的情况下，序列选择提供的非线性整形增益依然存在。