We study the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. Our perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, which was first proposed in [1], [2]. We consider the case when there is no shared randomness between the encoder and the decoder. For the case of discrete memoryless sources we derive a single-letter characterization of the RDP function, thus settling a problem that remains open for the marginal metric introduced in Blau and Michaeli [3] (with no shared randomness). Our achievability scheme is based on lossy source coding with a posterior reference map proposed in [4]. For the case of continuous valued sources under squared error distortion measure and squared quadratic Wasserstein perception measure we also derive a single-letter characterization and show that a noise-adding mechanism at the decoder suffices to achieve the optimal representation. For the case of zero perception loss, we show that our characterization interestingly coincides with the results for the marginal metric derived in [5], [6] and again demonstrate that zero perception loss can be achieved with a $3$-dB penalty in the minimum distortion. Finally we specialize our results to the case of Gaussian sources. We derive the RDP function for vector Gaussian sources and propose a waterfilling type solution. We also partially characterize the RDP function for a mixture of vector Gaussians.

翻译：我们研究了大块长渐近极限下无记忆信源模型的率失真感知（RDP）权衡。我们的感知测度基于文献[1]、[2]首次提出的条件于编码器输出的信源与重构序列分布之间的散度。我们考虑了编码器与解码器之间无共享随机性的情形。对于离散无记忆信源，我们推导了RDP函数的单字母表征，从而解决了文献[3]中Blau和Michaeli引入的边际度量（无共享随机性）下仍悬而未决的问题。我们的可达性方案基于文献[4]提出的带有后验参考映射的有损信源编码。对于平方误差失真测度和平方二次Wasserstein感知测度下的连续值信源，我们也推导了单字母表征，并证明解码器处的加噪机制足以实现最优表示。对于零感知损失情形，我们有趣地发现该表征与文献[5]、[6]中边际度量的结果一致，并再次论证了零感知损失可通过最小失真中3分贝的代价实现。最后，我们将结果特化为高斯信源情形：推导了向量高斯信源的RDP函数并提出注水型解，同时部分刻画了混合向量高斯信源的RDP函数。