Low-Complexity Geometric Shaping

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables store the constellation points bit labeling. To overcome these challenges, in this article, we study lattice-based geometrically shaped formats multidimensional Euclidean space. We describe evaluate fast low complexity algorithms that make practical, even with extremely high sizes more than 1028 points. The uncoded error rate performance of constellations is compared conventional quadrature amplitude modulate (QAM) additive white Gaussian noise nonlinear fiber channels. At a spectral efficiency 2 bits/sym/polarization, 4-QAM format, transmission reach improvement 38% shown at hard-decision forward correction threshold 2.26 × 10 -4 .