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.

翻译：针对平方误差失真度量这一特殊情况，分析了具有有限公共随机性的受限输出有损信源编码的失真率函数。当信源分布与重构分布均为高斯分布时，得到了该函数的显式表达式。这进一步部分刻画了感知度量由Kullback-Leibler散度或平方二次Wasserstein距离给定时，二次高斯率失真感知编码的信息论极限。