  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.
