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.

在大块长度的渐进极限中，我们研究了无记忆源模型的速率失真感知（RDP）权衡。我们的感知度量基于基于编码器输出条件下的源和重构序列的分布之间的离散，这最初是在 [1]，[2] 中提出的。我们考虑编码器和解码器之间没有共享随机性的情况。对于离散无记忆源的情况，我们导出了 RDP 函数的单字母特性，从而解决了在 Blau 和 Michaeli [3] 中引入的边际度量问题（无共享随机性）。我们的实现方案基于在 [4] 中提出的带后验参考映射的有损源编码。对于在平方误差失真度量和平方二次 Wasserstein 感知度量下的连续值源的情况，我们还导出了单字母特性，并表明在解码器中添加噪声机制足以实现最佳表示。对于零感知损失的情况，我们证明了我们的特征与在 [5]，[6] 中推导的边际度量结果有趣地相吻合，并再次证明了可以在最小失真中以 3 dB 的惩罚实现零感知损失。最后，我们将结果特化到高斯源的情况。我们导出了矢量高斯源的 RDP 函数并提出了一种水填充类型的解决方案。我们还部分表征了混合矢量高斯源的 RDP 函数。