Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation
Information TheoryMachine Learning
Summary
The authors explain an advanced theory called rate-distortion-perception (RDP) that expands on classic ideas about how much data is needed to compress information while keeping it accurate. They focus on how to also keep the compressed data looking or feeling realistic by measuring how similar the original and compressed versions are, beyond just simple errors. The tutorial covers mathematical tools and methods to calculate these limits for different kinds of data, especially when perception matters, and explores special cases where the math is simpler. Unlike other reviews that focus on AI models, the authors concentrate on the fundamental coding and optimization techniques behind these concepts. They also suggest future research areas combining information theory, neural networks, and perception-based systems.
Authors
Photios A. Stavrou, Giuseppe Serra, Marios Kountouris
Abstract
Classical rate-distortion (RD) theory has long established the fundamental limits of lossy compression by quantifying the minimum number of bits required to represent a source under a prescribed distortion constraint. However, widely used distortion measures such as mean-squared error often fail to capture perceptual quality or semantic validity, which are increasingly central in modern learning-driven applications. Rate-distortion-perception (RDP) theory extends the RD framework by introducing perception as a third fundamental axis, quantified via distributional similarity between the source and reconstructed signals, leading to the rate-distortion-perception function (RDPF). This tutorial provides a structured overview of the coding principles underlying perception-aware lossy compression and surveys recent achievability results under different randomness assumptions. It then presents a unifying optimization viewpoint for computing the RDPF as defined by Blau and Michaeli, for both discrete and continuous sources under broad families of perceptual constraints, including f-divergences, alpha-divergences, and Wasserstein-based metrics. Special attention is given to computational tools such as alternating minimization schemes, Newton-based methods, and convex optimization formulations, as well as to analytically tractable cases such as Gaussian sources and the perfect-realism regime. Unlike recent broad surveys that emphasize generative architectures and AI-empowered communication systems, this tutorial focuses on the coding-theoretic and computational machinery needed to characterize, compute, and interpret the RDP limits. Finally, the tutorial outlines promising research directions at the intersection of information theory, neural compression, robust source coding, and perception-aware networked control systems.