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).

The distortion-rate function of output-constrained lossy source coding with limited common randomness is analyzed for the special case of squared error distortion measure. An explicit expression is obtained when both source and reconstruction distributions are Gaussian. This further leads to a partial characterization of the information-theoretic limit of quadratic Gaussian rate-distortion-perception coding with the perception measure given by Kullback-Leibler divergence or squared quadratic Wasserstein distance.