Rate-Distortion-Perception Theory for the Quadratic Wasserstein Space

From a technical perspective, the n ew perception constraint is not conducive to single-letteriz ation; in fact, single-letterization appears to be impossi ble for a generic divergence φ. From an operational standpoint, it has been observed that u nder the perception constraint (8), the fundamental performance limits are generally not characterized by Blau and Michaeli's distortion-rate-perception function D (R,P); more surprisingly, they critically depend on the amount of commo n randomness shared between the encoder and decoder [5]-[8], whereas common randomness is known [4] to have no impact on th e performance limits under the perception constraint (7).