# A coding theorem for the rate-distortion-perception function

arXiv: https://arxiv.org/abs/2104.13662 · HTML: https://mlsanity.com/paper/2104.13662/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 28 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [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)
- [Real-Time Adaptive Image Compression](https://mlsanity.com/paper/1705.05823/) (2017)
- [Generative Compression](https://mlsanity.com/paper/1703.01467/) (2017)

## Built on by (most cited first, 30 of 30)

- [Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications](https://mlsanity.com/paper/2207.09353/) (2022)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [Multi-Realism Image Compression with a Conditional Generator](https://mlsanity.com/paper/2212.13824/) (2022)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [Neural Video Compression using GANs for Detail Synthesis and Propagation](https://mlsanity.com/paper/2107.12038/) (2021)
- [The Rate-Distortion-Perception Tradeoff: The Role of Common Randomness](https://mlsanity.com/paper/2202.04147/) (2022)
- [What makes an image realistic?](https://mlsanity.com/paper/2403.04493/) (2024)
- [Optimized Couplings for Watermarking Large Language Models](https://mlsanity.com/paper/2505.08878/) (2025)
- [Wasserstein Distortion: Unifying Fidelity and Realism](https://mlsanity.com/paper/2310.03629/) (2023)
- [Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure](https://mlsanity.com/paper/2401.12207/) (2024)
- [Conditional Perceptual Quality Preserving Image Compression](https://mlsanity.com/paper/2308.08154/) (2023)
- [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)
- [Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization](https://mlsanity.com/paper/2409.02388/) (2024)
- [You Cannot Feed Two Birds with One Score: the Accuracy-Naturalness Tradeoff in Translation](https://mlsanity.com/paper/2503.24013/) (2025)
- [Synonymous Variational Inference for Perceptual Image Compression](https://mlsanity.com/paper/2505.22438/) (2025)
- [Rate-Distortion-Perception Theory for Semantic Communication](https://mlsanity.com/paper/2312.05437/) (2023)
- [Optimal Neural Compressors for the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2503.17558/) (2025)
- [Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space](https://mlsanity.com/paper/2504.17236/) (2025)
- [Characterization of the Distortion-Perception Tradeoff for Finite Channels with Arbitrary Metrics](https://mlsanity.com/paper/2402.02265/) (2024)
- [Alternating Minimization Schemes for Computing Rate-Distortion-Perception Functions with f-Divergence Perception Constraints](https://mlsanity.com/paper/2408.15015/) (2024)
- [Advances in Diffusion-Based Generative Compression](https://mlsanity.com/paper/2601.18932/) (2026)
- [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)
- [A Synonymous Variational Perspective on the Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/2604.14603/) (2026)
- [Secure Rate-Distortion-Perception: A Randomized Distributed Function Computation Approach for Realism](https://mlsanity.com/paper/2604.20245/) (2026)
- [Trustworthy AI: Ensuring Reliability and Accountability from Models to Agents](https://mlsanity.com/paper/2605.08964/) (2026)
- [Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation](https://mlsanity.com/paper/2607.17232/) (2026)
- [The Hidden Perception Constraint in Task-Aware Compression](https://mlsanity.com/paper/2609.35684/) (2026)

## Abstract (arXiv)

The rate-distortion-perception function (RDPF; Blau and Michaeli, 2019) has emerged as a useful tool for thinking about realism and distortion of reconstructions in lossy compression. Unlike the rate-distortion function, however, it is unknown whether encoders and decoders exist that achieve the rate suggested by the RDPF. Building on results by Li and El Gamal (2018), we show that the RDPF can indeed be achieved using stochastic, variable-length codes. For this class of codes, we also prove that the RDPF lower-bounds the achievable rate