  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.
