End-to-End Learning of Probabilistic Constellation Shaping through Importance Sampling

2025-06-19

AI Summary

This work addresses the challenge in probabilistic constellation shaping (PCS) for coded modulation systems, where end-to-end learning traditionally requires manual derivation of gradient terms—error-prone and lacking generalizability. We propose a novel mutual information-driven loss function leveraging importance sampling and automatic differentiation. Our method eliminates the need for hand-crafted analytical gradients of probability mass functions, theoretically guaranteeing unbiased gradient estimation while enabling flexible rate adaptation and approaching Shannon capacity. The framework integrates a deep autoencoder architecture, probabilistic shaping modeling, and differentiable channel simulation. Evaluated on both AWGN and intensity-modulation direct-detection (IM-DD) channels, it achieves performance competitive with state-of-the-art approaches, thereby validating both gradient accuracy and cross-channel generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual information. The optimization problem is however challenging even for simple channel models. While autoencoder-based machine learning has been applied successfully to solve this problem [1], it requires manual computation of additional terms for the gradient which is an error-prone task. In this work, we present novel loss functions for autoencoder-based learning of probabilistic constellation shaping for coded modulation systems using automatic differentiation and importance sampling. We show analytically that our proposed approach also uses exact gradients of the constellation point probabilities for the optimization. In simulations, our results closely match the results from [1] for the additive white Gaussian noise channel and a simplified model of the intensity-modulation direct-detection channel.

Problem

• Optimizing constellation point probabilities for mutual information
• Overcoming gradient computation challenges in autoencoder-based learning
• Validating novel loss functions for probabilistic constellation shaping

Innovation

• Autoencoder-based learning with novel loss functions
• Uses automatic differentiation and importance sampling
• Optimizes exact gradients of constellation probabilities