Probabilistic Shaping Four-dimensional Modulation with Soft Decision for Self-Homodyne Coherent Detection Systems

We demonstrate a probabilistic shaping (PS) four-dimensional (4D) modulation in self-homodyne coherent transmission system. The 4D modulation is based on inter-symbol amplitude translation (AT) to perform set partitioning. The distribution of constellation points after AT is optimized by de-DC. The parity bits produced by the AT are transmitted with the pilot tone by remapping. In addition, a soft decision for this 4D-PS signal is proposed. An experiment of self-homodyne coherent ultra-high order 4D signal transmission based on two cores of a 7-core fiber is demonstrated with a spectral efficiency of 16.37 bit/s/Hz. The 4D signals with soft decision can provide up to 0.78 bit/symbol and 1.85 bit/symbol gain compared to normal polarization division multiplexing signals and hard-decision 4D signals.