Orthant-Symmetric Multi-dimensional Geometrically-Shaped Modulation Optimization

Generalized mutual information is used to design geometrically-shaped modulations based on orthant-symmetric (OS) constraint. Numerical results show that the time-saving of the OS-based optimization over standard optimization is approximately a factor of 4 to 10 at medium to high signal-to-noise ratios (SNRs). Furthermore, the proposed 4D-OS modulation formats provides gains of up to 0.8 dB over the conventional SP-128QAM at the same information rate.