Power-Efficient Voronoi Constellations for Fiber-Optic Communication Systems

Voronoi constellations (VCs) are considered as an effective geometric shaping method due to their high power efficiencies and low complexity. In this paper, the performance of 16- and 32-dimensional VCs with a variety of spectral efficiencies transmitted in the nonlinear fiber channel are investigated. Both single-channel and wavelength-division multiplexing systems are considered for the transmission of the VCs, as well as different signal processing schemes, including chromatic dispersion compensation and digital backpropagation. Multiple performance metrics including the uncoded bit error rate, mutual information (MI), and generalized mutual information (GMI) of VCs are evaluated. Compared with quadrature amplitude modulation (QAM) formats, the VCs provide 1.0–2.4 dB launch power gains, up to 0.50 bits/symbol/dimension-pair MI gains, up to around 30% potential reach increase at the same MI, and up to 0.30 bits/symbol/dimension-pair GMI gains in a limited launch power range. The observed performance gains over QAM are found higher than in the back-to-back case. Moreover, a general GMI estimation method for very large constellations using importance sampling is proposed for the first time.