Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

End-to-End Learning of Geometrical Shaping Maximizing Generalized Mutual Information

Kadir Gümüs, Alex Alvarado, Bin Chen, Christian Häger, Erik Agrell

TL;DR

This paper tackles the nonconvexity of GMI-based end-to-end learning for geometric shaping in optical communications. It shows that standard AE optimization is prone to poor local optima and that domain-specific initialization, especially Gray-labeled constellations, is essential. The authors propose a fast coordinate-optimization approach—eliminating hidden layers so constellation coordinates are directly optimized—initialized with Gray-labeled APSK and evaluated with Gauss-Hermite quadratures. The method delivers state-of-the-art geometrical constellations up to M=1024 in 2D and M=64 in 4D, with SNR gains up to about 1 dB and reach gains up to 26% over QAM, while significantly reducing computation time, highlighting practical impact for high-rate, fiber-optic systems.

Abstract

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26\% w.r.t. to QAM.

End-to-End Learning of Geometrical Shaping Maximizing Generalized Mutual Information

TL;DR

This paper tackles the nonconvexity of GMI-based end-to-end learning for geometric shaping in optical communications. It shows that standard AE optimization is prone to poor local optima and that domain-specific initialization, especially Gray-labeled constellations, is essential. The authors propose a fast coordinate-optimization approach—eliminating hidden layers so constellation coordinates are directly optimized—initialized with Gray-labeled APSK and evaluated with Gauss-Hermite quadratures. The method delivers state-of-the-art geometrical constellations up to M=1024 in 2D and M=64 in 4D, with SNR gains up to about 1 dB and reach gains up to 26% over QAM, while significantly reducing computation time, highlighting practical impact for high-rate, fiber-optic systems.

Abstract

GMI-based end-to-end learning is shown to be highly nonconvex. We apply gradient descent initialized with Gray-labeled APSK constellations directly to the constellation coordinates. State-of-the-art constellations in 2D and 4D are found providing reach increases up to 26\% w.r.t. to QAM.

Paper Structure

This paper contains 4 sections, 2 figures.

Table of Contents

  1. Introduction
  2. End-to-End Autoencoder Learning Based on GMI
  3. Proposed Approach to GMI-Based Geometric Shaping
  4. Conclusions

Figures (2)

  • Figure 1: Left: Block diagram of the transmitter NN for GMI-based end-to-end learning; red arrows illustrate three ways to compute the loss function for optimizing the NN parameters. Right: Empirical CDF of the AE results assuming $200$ random starting points, where $M=16$, $N=2$, $\text{SNR} = 9\,$dB (Cyclical: cyclical learning rate, BSA: binary switching algorithm, QAM init.: initialization with Gray-labeled $16$-QAM).
  • Figure 2: Results for $N=2$, $M=1024$ (left), $N=2$, $M=256$ (center), and $N=4$, $M=64$ (right), where the optimization is done separately for each SNR. SNR gains are with respect to QAM and measured assuming a binary FEC with rate $0.8$ (dotted lines). The amount of rings for the initial APSK constellations are 16, 8 and 1, respectively (left to right). Gains with respect to prior works are $0.14$ dB, $0.12$ dB, and $0.13$ dB, respectively. The reach increases are calculated according to the GN model PoggioliniJLT2014 based on a multi-span optical link with SSMF, 45 GBaud symbol rate, and 11 WDM channels. The length of a span is 80 km and EDFA noise figure is 4.5 dB.