Recent advances in machine learning-aided lossy compression are incorporating perceptual fidelity into the rate-distortion theory. In this paper, we study the rate-distortion-perception trade-off when the perceptual quality is measured by the total variation distance between the empirical and product distributions of the discrete memoryless source and its reconstruction. We consider the general setting, where two types of resources are available at both the encoder and decoder: a common side information sequence, correlated with the source sequence, and common randomness. We show that the region under the strong perceptual constraint is a subset of that for the weaker empirical perceptual constraint. When sufficient common randomness is provided, the required communication rate is the minimum conditional mutual information such that the distortion and perceptual constraints are satisfied. The coding scheme in the proof of achievability takes advantage of the likelihood encoder.

翻译：近年来，机器学习辅助有损压缩的进展将感知保真度纳入了率失真理论。本文研究了当感知质量通过离散无记忆信源及其重建的经验分布与乘积分布之间的总变差距离衡量时，率-失真-感知权衡问题。我们考虑一般设定，其中编码器和解码器均拥有两种可用资源：与信源序列相关的公共边信息序列以及公共随机性。研究表明，在强感知约束下的可行区域是弱经验感知约束下的子集。当提供足够的公共随机性时，所需通信速率是满足失真与感知约束的最小条件互信息量。可达性证明中的编码方案利用了似然编码器。