We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, $f$-separable distortion measure and study its implications on the characterization of the minimum achievable rates (also called $f$-separable indirect rate distortion function (iRDF)) under both excess and average distortion constraints. First, we provide a single-letter characterization of the optimal rates subject to an excess distortion using properties of the $f$-separable distortion. Our main result is a single-letter characterization of the $f$-separable iRDF subject to an average distortion constraint. As a consequence of the previous results, we also show a series of equalities that hold using either indirect or classical RDF under $f$-separable excess or average distortions. We corroborate our results with two application examples in which new closed-form solutions are derived, and based on these, we also recover known special cases.

翻译：我们考虑一个受{失真函数}约束的远程信源编码问题。与经典的可分离失真准则不同，本文采用更一般的$f$-可分失真度量，并研究其在超额失真和平均失真约束下对最小可达速率（也称为$f$-可分间接率失真函数(iRDF)）表征的影响。首先，利用$f$-可分失真的性质，我们给出了超额失真约束下最优速率的单字母表征。主要结果是得到了平均失真约束下$f$-可分间接率失真函数的单字母表征。作为上述结论的推论，我们还证明了一系列在$f$-可分超额或平均失真条件下，使用间接或经典率失真函数时成立的等式。通过两个应用实例验证了我们的结果，其中推导出了新的闭式解，并基于这些解恢复了已知的特例。