Abstract

We discuss shaping with continuous and discrete input distributions for the Stokes vector receiver (SVR). We use the Forney method to derive tight analytical approximations to the optimal continuous input distribution at high signal-to-noise ratio (SNR). The Forney method analysis finds that an exponential distribution in the intensity (corresponding to the Stokes parameter $S_{0}$ ) is the optimal continuous input distribution for thermal noise-limited and amplifier noise-limited SVRs, providing ultimate shape gains of $1.056$ dB and $\pi e / 6\approx 1.533$ dB, respectively. We also perform numerical studies of discrete input distributions obtained using the Blahut-Arimoto method or by sampling analytically derived continuous distributions. We find that a sampled exponential distribution in the intensity provides $0.078$ dB and $0.165$ dB higher shape gains than a sampled Gaussian distribution of the SV in the thermal noise-limited and amplifier noise-limited regimes, respectively. We also compare the performance of the SVR to that of a dual-polarization coherent receiver. We show that, owing to noise enhancement, the SVR incurs an SNR penalty of about $5.5$ dB with respect to a coherent system that modulates three of the four available degrees of freedom.