# The Rate-Distortion-Perception Trade-off: The Role of Private Randomness

arXiv: https://arxiv.org/abs/2404.01111 · HTML: https://mlsanity.com/paper/2404.01111/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 1 Apr 2024.

## Builds on (most cited first, 11 of 11)

- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Universally Quantized Neural Compression](https://mlsanity.com/paper/2006.09952/) (2020)
- [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)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [Compression with Exact Error Distribution for Federated Learning](https://mlsanity.com/paper/2310.20682/) (2023)
- [Communication Efficient Private Federated Learning Using Dithering](https://mlsanity.com/paper/2309.07809/) (2023)
- [Wasserstein Distortion: Unifying Fidelity and Realism](https://mlsanity.com/paper/2310.03629/) (2023)

## Built on by (most cited first, 6 of 6)

- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2503.17558/) (2025)
- [Constrained Gaussian Wasserstein Optimal Transport with Commutative Covariance Matrices](https://mlsanity.com/paper/2503.03744/) (2025)
- [Training-Free Rate-Distortion-Perception Traversal With Diffusion](https://mlsanity.com/paper/2603.04005/) (2026)
- [Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism](https://mlsanity.com/paper/2604.20245/) (2026)
- [TriDP-PTM: a three-stage distortion-perception tradeoff guides the pre-training model for radar cardiac sensing](https://mlsanity.com/paper/2605.25725/) (2026)

## Abstract (arXiv)

In image compression, with recent advances in generative modeling, the existence of a trade-off between the rate and the perceptual quality (realism) has been brought to light, where the realism is measured by the closeness of the output distribution to the source. It has been shown that randomized codes can be strictly better under a number of formulations. In particular, the role of common randomness has been well studied. We elucidate the role of private randomness in the compression of a memoryless source Xn=(X1,...,Xn) under two kinds of realism constraints. The near-perfect realism constraint requires the joint distribution of output symbols (Y1,...,Yn) to be arbitrarily close the distribution of the source in total variation distance (TVD). The per-symbol near-perfect realism constraint requires that the TVD between the distribution of output symbol Yt and the source distribution be arbitrarily small, uniformly in the index t. We characterize the corresponding asymptotic rate-distortion trade-off and show that encoder private randomness is not useful if the compression rate is lower than the entropy of the source, however limited the resources in terms of common randomness and decoder private randomness may be.