Fiber Nonlinearity Mitigation by Short-Length Probabilistic Constellation Shaping for Pilot-Aided Signaling

Probabilistic constellation shaping (PCS) offers a significant performance improvement over uniform signaling. It was recently discovered that long blocks are not required to achieve maximum shaping gain when transmitting over the nonlinear fiber channel because short-length PCS effectively mitigates fiber nonlinear interference (NLI). The reason for this behavior is that short-length PCS implicitly induces some temporal properties in the shaped transmit sequence that are beneficial for the fiber-optic channel. To achieve robust data-aided digital signal processing of high-order QAM, periodic quaternary phase shift keying pilots are typically inserted into the high-order QAM transmit sequence. In this work, we investigate in simulations the effect of such pilot-aided signaling on NLI mitigation. Albeit modifying the temporal properties of the shaped transmit sequence, a pilot rate of 1/32 is found to not alter the beneficial effects of short-length PCS. The operation meaning of this finding is that even with pilot-aided signaling, long PCS block lengths are not required for maximum shaping gain.