Abstract

We proposean optimization scheme to maximize symbol-wise mutual information (MI) of the amplitude-phase shift keying (APSK) constellations. We optimize APSK constellations for the additive white Gaussian noise (AWGN) channel and non-linear fiber channel. For the fiber channel, the optimization is based on the enhanced Gaussian noise (EGN) model and is performed at the maximum modified signal-to-noise ratio (SNR) of the optical system. By doing so, our optimization algorithm maximizes the MI rate while the impacts of shaping on the non-linear interference noise (NLIN) power are considered. Our results show that by optimizing APSK constellations specifically for the fiber channel, significant reach improvements can be achieved. In addition, by using the mutual information formula and assuming a model for the radius of the APSK rings, we obtain an equation that provides the optimal APSK radii based on that model. After demonstrating the accuracy of this model, we compare the optimized APSKs of the AWGN and fiber channel and show that in the AWGN channels, the optimal radius of the rings grows with the ring number faster than the radii of the APSKs optimized for the fiber channel. Our results indicate that in the highly non-linear regimes of the fiber channel, geometric shaping has to be performed for the fiber since AWGN-based shaping gives poor performance.

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