Probabilistic Shaping for the Optical Phase Conjugation Channel

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGN-like transmission strategies thus remain effective. A channel-agnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After $\approx$ 2000 km of transmission, mid-link OPC is demonstrated to provide $\approx$ 1 dB of gain in effective SNR, which translates to $\approx$ 0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra $\approx$ 0.2 bits/QAM symbol by applying probabilistic shaping.