Rate-Distortion-Perception Trade-Off With Strong Realism Constraints: Role of Side Information and Common Randomness

In image compression, with recent advances in generative modeling, existence of a trade-off between rate and perceptual quality has been brought to light, where perceptual quality is measured by the closeness of the output and source distributions. We consider the compression of a memoryless source sequenceXn= (X1, . . . ,Xn) in the presence of memoryless side informationZn= (Z1, . . . ,Zn), originally studied by Wyner and Ziv, but elucidate the impact of astrong perfect realismconstraint, which requires the joint distribution of output symbolsYn= (Y1, ...,Yn) to match the distribution of the source sequence. We consider two cases: whenZnis available only at the decoder, or at both the encoder and decoder, and characterize the information theoretic limits in both scenarios. Previous works show the superiority of randomized codes under strong perceptual quality constraints. WhenZnis available at both terminals, we characterize its dual role, as a source of common randomness, and as a second look on the source for the receiver. We also study different notions of strong perfect realism, which we callmarginal realism, joint realismandnear-perfect realism. We derive explicit solutions whenXandZare jointly Gaussian under the squared error distortion measure. In traditional lossy compression, havingZonly at the decoder imposes no rate penalty in the Gaussian scenario. We show that, when strong perfect realism constraints are imposed this holds only when sufficient common randomness is available.