Probabilistic Shaping for Rotationally Symmetrical Two-Dimensional Constellations

A ring-based constant composition distribution matcher (R-CCDM) is designed for shaping rotationally symmetrical two-dimensional (RS-2D) constellations. The procedure of distribution matching can be divided into two steps. First, nonuniformly distributed rings are generated by CCDM to approach a probability distribution calculated from that of modulation symbols. Second, a uniform mapping is performed to select one amplitude signal point from each ring. Compared with CCDM, the proposed DM contains multiple amplitude compositions, and hence achieves less rate loss. Numerical results show that, at moderate spectral efficiency, probabilistic shaping with R-CCDM outperforms that with CCDM by about $0.2 \sim 0.3 \mathrm{~dB}$ for different modulation formats.