# Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization

arXiv: https://arxiv.org/abs/2409.02388 · HTML: https://mlsanity.com/paper/2409.02388/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 4 Sep 2024.

## Builds on (most cited first, 16 of 16)

- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [A Theory of the Distortion-Perception Tradeoff in Wasserstein Space](https://mlsanity.com/paper/2107.02555/) (2021)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [A coding theorem for the rate-distortion-perception function](https://mlsanity.com/paper/2104.13662/) (2021)
- [On the advantages of stochastic encoders](https://mlsanity.com/paper/2102.09270/) (2021)
- [On Perceptual Lossy Compression: The Cost of Perceptual Reconstruction and An Optimal Training Framework](https://mlsanity.com/paper/2106.02782/) (2021)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Optimally Controllable Perceptual Lossy Compression](https://mlsanity.com/paper/2206.10082/) (2022)
- [On the Choice of Perception Loss Function for Learned Video Compression](https://mlsanity.com/paper/2305.19301/) (2023)
- [Information Constrained Optimal Transport: From Talagrand, to Marton, to Cover](https://mlsanity.com/paper/2008.10249/) (2020)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [The Rate-Distortion-Perception Trade-off: The Role of Private Randomness](https://mlsanity.com/paper/2404.01111/) (2024)
- [On the Computation of the Gaussian Rate-Distortion-Perception Function](https://mlsanity.com/paper/2311.09190/) (2023)
- [Output-Constrained Lossy Source Coding With Application to Rate-Distortion-Perception Theory](https://mlsanity.com/paper/2403.14849/) (2024)
- [Characterization of the Distortion-Perception Tradeoff for Finite Channels with Arbitrary Metrics](https://mlsanity.com/paper/2402.02265/) (2024)

## Built on by (most cited first, 4 of 4)

- [Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space](https://mlsanity.com/paper/2504.17236/) (2025)
- [Constrained Gaussian Wasserstein Optimal Transport with Commutative Covariance Matrices](https://mlsanity.com/paper/2503.03744/) (2025)
- [Easz: An Agile Transformer-based Image Compression Framework for Resource-constrained IoTs](https://mlsanity.com/paper/2505.01742/) (2025)
- [Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation](https://mlsanity.com/paper/2607.17232/) (2026)

## Abstract (arXiv)

This paper investigates the best known bounds on the quadratic Gaussian distortion-rate-perception function with limited common randomness for the Kullback-Leibler divergence-based perception measure, as well as their counterparts for the squared Wasserstein-2 distance-based perception measure, recently established by Xie et al. These bounds are shown to be nondegenerate in the sense that they cannot be deduced from each other via a refined version of Talagrand's transportation inequality. On the other hand, an improved lower bound is established when the perception measure is given by the squared Wasserstein-2 distance. In addition, it is revealed by exploiting the connection between rate-distortion-perception coding and entropy-constrained scalar quantization that all the aforementioned bounds are generally not tight in the weak perception constraint regime.