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 nonlinear probabilistic shaping. 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：概率整形是一种提高相干光通信系统性能的实用方法。在非线性区域，概率整形提供的优势可能因获得额外非线性整形增益的机会而增加。遗憾的是，传统整形技术（如概率幅度整形，PAS）的优化仅在有限的实际应用场景中能产生显著的非线性整形增益。本文利用序列选择研究非线性概率整形的潜力、机遇和挑战。首先，我们证明理想序列选择相比优化块长度的PAS能够提供高达0.13 bit/s/Hz的增益。然而，这种额外增益仅在选择度量考虑符号正负性时才能获得：尽管无需对符号进行整形，但必须已知符号信息以计算选择度量。此外，我们表明选择对符号速率和链路长度的依赖性非关键：当这些参数改变时，为特定场景选择的序列仍能提供相关增益。接着，我们分析并比较了若干序列选择的实际实现方案，同时考虑其与前向纠错（FEC）的交互及复杂度。总体而言，单块和多块FEC独立比特加扰是最佳方案，可实现高达0.08 bit/s/Hz的增益。其实际实现的主要挑战和限制仍在于度量评估，当前复杂度过高。最后，我们证明当包含载波相位恢复时，序列选择提供的非线性整形增益依然保持。