Low-Complexity Geometric Shaping

TL;DR

This paper introduces low-complexity lattice-based geometric shaping formats for high-dimensional modulation, significantly improving transmission reach over traditional QAM in fiber channels.

Contribution

It proposes fast, low-complexity algorithms for lattice-based geometric shaping with extremely large constellations, enabling practical implementation and improved performance.

Findings

Achieves over 38% longer transmission reach at 2 bits/sym/polarization.

Demonstrates comparable bit error rate performance to QAM in fiber channels.

Provides scalable algorithms for high-dimensional geometric modulation.

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 $2.26\times 10^{-4}$.