# Generative AI-Based Probabilistic Constellation Shaping With Diffusion Models

arXiv: https://arxiv.org/abs/2311.09349 · HTML: https://mlsanity.com/paper/2311.09349/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion for compression and wireless, one of 14 directions in Diffusion models.
- Builds on 31 of its 34 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Placed in

- Diffusion models / [Diffusion for compression and wireless](https://mlsanity.com/diffusion/diffusion-for-compression-and-wireless/)

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models](https://mlsanity.com/paper/2210.08933/) (2022)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Sionna: An Open-Source Library for Next-Generation Physical Layer Research](https://mlsanity.com/paper/2203.11854/) (2022)
- [Generative AI](https://mlsanity.com/paper/2309.07930/) (2023)
- [Toward a 6G AI-Native Air Interface](https://mlsanity.com/paper/2012.08285/) (2020)
- [DeepRx: Fully Convolutional Deep Learning Receiver](https://mlsanity.com/paper/2005.01494/) (2020)
- [Model-free Training of End-to-end Communication Systems](https://mlsanity.com/paper/1812.05929/) (2018)
- [SwinGNN: Rethinking Permutation Invariance in Diffusion Models for Graph Generation](https://mlsanity.com/paper/2307.01646/) (2023)
- [Massive Access for 5G and Beyond](https://mlsanity.com/paper/2002.03491/) (2020)
- [High Perceptual Quality Wireless Image Delivery with Denoising Diffusion Models](https://mlsanity.com/paper/2309.15889/) (2023)
- [CDDM: Channel Denoising Diffusion Models for Wireless Communications](https://mlsanity.com/paper/2305.09161/) (2023)
- [Twelve Scientific Challenges for 6G: Rethinking the Foundations of Communications Theory](https://mlsanity.com/paper/2207.01843/) (2022)
- [MRI Reconstruction with Side Information using Diffusion Models](https://mlsanity.com/paper/2303.14795/) (2023)
- [6G White Paper on Machine Learning in Wireless Communication Networks](https://mlsanity.com/paper/2004.13875/) (2020)
- [CommIN: Semantic Image Communications as an Inverse Problem with INN-Guided Diffusion Models](https://mlsanity.com/paper/2310.01130/) (2023)
- [Joint Learning of Geometric and Probabilistic Constellation Shaping](https://mlsanity.com/paper/1906.07748/) (2019)
- [Waveform Learning for Next-Generation Wireless Communication Systems](https://mlsanity.com/paper/2109.00998/) (2021)
- [Score-Based Generative Models for Robust Channel Estimation](https://mlsanity.com/paper/2111.08177/) (2021)
- [Waveform Learning for Reduced Out-of-Band Emissions Under a Nonlinear Power Amplifier](https://mlsanity.com/paper/2201.05524/) (2022)
- [DeepTx: Deep Learning Beamforming with Channel Prediction](https://mlsanity.com/paper/2202.07998/) (2022)
- [Diffusion Models for Accurate Channel Distribution Generation](https://mlsanity.com/paper/2309.10505/) (2023)
- [End-to-end Waveform Learning Through Joint Optimization of Pulse and Constellation Shaping](https://mlsanity.com/paper/2106.15158/) (2021)

## Built on by (most cited first, 2 of 2)

- [Diffusion Model Based Resource Allocation Strategy in Ultra-Reliable Wireless Networked Control Systems](https://mlsanity.com/paper/2407.15784/) (2024)
- [Deep-Learned Compression for Radio-Frequency Signal Classification](https://mlsanity.com/paper/2403.03150/) (2024)

## Abstract (arXiv)

Diffusion models are at the vanguard of generative AI research with renowned solutions such as ImageGen by Google Brain and DALL.E 3 by OpenAI. Nevertheless, the potential merits of diffusion models for communication engineering applications are not fully understood yet. In this paper, we aim to unleash the power of generative AI for PHY design of constellation symbols in communication systems. Although the geometry of constellations is predetermined according to networking standards, e.g., quadrature amplitude modulation (QAM), probabilistic shaping can design the probability of occurrence (generation) of constellation symbols. This can help improve the information rate and decoding performance of communication systems. We exploit the ``denoise-and-generate'' characteristics of denoising diffusion probabilistic models (DDPM) for probabilistic constellation shaping. The key idea is to learn generating constellation symbols out of noise, ``mimicking'' the way the receiver performs symbol reconstruction. This way, we make the constellation symbols sent by the transmitter, and what is inferred (reconstructed) at the receiver become as similar as possible, resulting in as few mismatches as possible. Our results show that the generative AI-based scheme outperforms deep neural network (DNN)-based benchmark and uniform shaping, while providing network resilience as well as robust out-of-distribution performance under low-SNR regimes and non-Gaussian assumptions. Numerical evaluations highlight 30% improvement in terms of cosine similarity and a threefold improvement in terms of mutual information compared to DNN-based approach for 64-QAM geometry.