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Probabilisticshaping is, nowadays, a pragmatic and popular approach to improve the performance of coherent optical fiber communication systems. In the linear regime, the potential of probabilistic shaping in terms of shaping gain and rate granularity is well known, and its practical implementation has been mostly mastered. In the nonlinear regime, the advantages offered by probabilistic shaping remain not only valid, but might also increase thanks to the appealing opportunity to use the same technique to mitigate nonlinear effects and obtain an additional nonlinear shaping gain. Unfortunately, despite the recent research efforts, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in particular scenarios of limited practical interest, e.g., in the absence of carrier phase recovery. Recently, a more theoretical approach …