In image compression, with recent advances in generative modeling, the existence of a trade-off between the rate and the perceptual quality has been brought to light, where the perception is measured by the closeness of the output distribution to the source. This leads to the question: how does a perception constraint impact the trade-off between the rate and traditional distortion constraints, typically quantified by a single-letter distortion measure? We consider the compression of a memoryless source $X$ in the presence of memoryless side information $Z,$ studied by Wyner and Ziv, but elucidate the impact of a perfect realism constraint, which requires the output distribution to match the source distribution. We consider two cases: when $Z$ is available only at the decoder or at both the encoder and the decoder. The rate-distortion trade-off with perfect realism is characterized for sources on general alphabets when infinite common randomness is available between the encoder and the decoder. We show that, similarly to traditional source coding with side information, the two cases are equivalent when $X$ and $Z$ are jointly Gaussian under the squared error distortion measure. We also provide a general inner bound in the case of limited common randomness.

翻译：在图像压缩领域，随着生成建模的最新进展，速率与感知质量之间的权衡关系已被揭示，其中感知质量通过输出分布与源分布的接近程度来衡量。这引出一个问题：感知约束如何影响速率与传统失真约束（通常由单字母失真度量量化）之间的权衡？本文考虑在存在无记忆边信息$Z$的情况下对无记忆源$X$进行压缩，这一场景由Wyner和Ziv研究，但本文阐明了完美真实感约束（要求输出分布与源分布匹配）的影响。我们研究了两种情况：当$Z$仅解码器可用，以及编码器和解码器均可用时。在编码器与解码器之间具有无限公共随机性的条件下，针对一般字母表上的源，刻画了具有完美真实感的速率-失真权衡。结果表明，与传统的含边信息信源编码类似，当$X$和$Z$为联合高斯分布且采用平方误差失真度量时，上述两种情况等价。此外，在有限公共随机性情形下，我们给出了一个通用内界。