Low-Complexity Geometric Shaping

Abstract

Approaching Shannon's capacity via geometric shaping has usually been regarded as challenging due to modulation and demodulation complexity, requiring look-up tables to store the constellation points and constellation bit labeling. To overcome these challenges, in this paper, we study lattice-based geometrically shaped modulation formats in multidimensional Euclidean space. We describe and evaluate fast and low complexity modulation and demodulation algorithms that make these modulation formats practical, even with extremely high constellation sizes with more than $10^{28}$ points. The uncoded bit error rate performance of these constellations is compared with the conventional QAM formats in the additive white Gaussian noise and nonlinear fiber channels. At a spectral efficiency of 2 bits/sym/polarization, compared with 4-QAM format, transmission reach improvement of more than 38% is shown at the hard-decision forward error correction threshold of $2.26\times 10^{-4}$.

References in corpus (6)

• On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel
• Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations
• LDPC Coded Modulation with Probabilistic Shaping for Optical Fiber Systems
• Demonstration of an 8D Modulation Format with Reduced Inter-Channel Nonlinearities in a Polarization Multiplexed Coherent System
• A Pragmatic Coded Modulation Scheme for High-Spectral-Efficiency Fiber-Optic Communications
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Cited by in corpus (3)

• Geometrically-Shaped Multi-Dimensional Modulation Formats in Coherent Optical Transmission Systems
• Low-complexity Voronoi shaping for the Gaussian channel
• Low-Complexity Geometrical Shaping for 4D Modulation Formats via Amplitude Coding