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：概率整形是提升相干光通信系统性能的一种实用方法。在非线性机制下，由于有机会获得额外的非线性整形增益，概率整形所提供的优势可能会增加。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才能产生相关的非线性整形增益。本文利用序列选择方法，探索了概率整形在非线性信道中的潜力、机遇与挑战。首先，我们证明，相较于采用优化块长度的PAS，理想序列选择能够提供高达0.13比特/秒/赫兹的增益。然而，这种额外增益仅在选择度量考虑符号符号极性时才能获得：计算选择度量时需知晓符号极性，但无需对其进行整形。此外，研究表明，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场景参数改变时仍能提供相关增益。随后，我们通过考虑与前向纠错（FEC）的交互及复杂度，分析并比较了多种序列选择的实际实现方案。总体而言，单块和多块独立于FEC的比特加扰是最佳选择，可获得高达0.08比特/秒/赫兹的增益。其实际实现的主要挑战与限制仍在于度量评估，目前其复杂度过高。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存在。