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 consider both the strong perceptual constraint and the weaker empirical perceptual constraint. The required communication rate for achieving the distortion and empirical perceptual constraint is the minimum conditional mutual information, and similar result holds for strong perceptual constraint when sufficient common randomness is provided and the output along with the side information is constraint to an independent and identically distributed sequence.

翻译：近期机器学习辅助有损压缩的进展将感知保真度纳入了速率-失真理论。本文研究当感知质量由离散无记忆信源及其重建序列的经验分布与乘积分布之间的总变差距离衡量时，速率-失真-感知三者的权衡关系。我们考虑一般场景：编码器和解码器均配备两种资源——与信源序列相关的公共边信息序列和公共随机性。我们分别考虑强感知约束和弱经验感知约束两种情况。实现失真与经验感知约束所需的通信速率为最小条件互信息；当提供充足公共随机性且输出与边信息共同受限于独立同分布序列时，强感知约束下的结论与此类似。