On the Rate-Distortion-Perception Function

TL;DR

This paper extends rate-distortion theory by incorporating perceptual quality constraints, demonstrating that deterministic codes can achieve the new rate-distortion-perception limits in most cases, and clarifying key conceptual differences.

Contribution

It shows that deterministic coding schemes are sufficient for achieving the rate-distortion-perception function, clarifies differences in perceptual quality notions, and explores alternative perception constraints.

Findings

Deterministic codes can achieve the rate-distortion-perception function in most cases.

The paper clarifies differences between notions of perfect perceptual quality.

It explores alternative formulations of the perception constraint.

Abstract

Rate-distortion-perception theory generalizes Shannon's rate-distortion theory by introducing a constraint on the perceptual quality of the output. The perception constraint complements the conventional distortion constraint and aims to enforce distribution-level consistencies. In this new theory, the information-theoretic limit is characterized by the rate-distortion-perception function. Although a coding theorem for the rate-distortion-perception function has recently been established, the fundamental nature of the optimal coding schemes remains unclear, especially regarding the role of randomness in encoding and decoding. It is shown in the present work that except for certain extreme cases, the rate-distortion-perception function is achievable by deterministic codes. This paper also clarifies the subtle differences between two notions of perfect perceptual quality and explores some alternative formulations of the perception constraint.