抽象字母上非预期RDF的最优非平稳再现分布
Optimal Nonstationary Reproduction Distribution for Nonanticipative RDF on Abstract Alphabets
AI总结：
本文定义了抽象字母上的非预期率失真函数，利用概率测度的弱收敛性证明其性质，并给出了最优非平稳再现分布的闭式表达式。
摘要：
本文引入了抽象字母上非预期率失真函数（RDF）的定义，并利用概率测度的弱收敛性展示了其各种性质，例如最优再现条件分布的存在性、保真度集的紧性、RDF泛函的下半连续性等。此外，我们推导了最优非平稳再现分布的闭式表达式。该表达式通过时间向后递归计算。在整篇文章中，我们通过回顾文献\cite{tatikonda2000}中推导的编码定理，指出了非预期RDF的操作意义，并阐述了与Gorbunov-Pinsker的非预期$\varepsilon$-熵\cite{gorbunov-pinsker}的关系。
英文摘要：
In this paper we introduce a definition for nonanticipative Rate Distortion Function (RDF) on abstract alphabets, and we invoke weak convergence of probability measures to show various of its properties, such as, existence of the optimal reproduction conditional distribution, compactness of the fidelity set, lower semicontinuity of the RDF functional, etc. Further, we derive the closed form expression of the optimal nonstationary reproduction distribution. This expression is computed recursively backward in time. Throughout the paper we point out an operational meaning of the nonanticipative RDF by recalling the coding theorem derive in \cite{tatikonda2000}, and we state relations to Gorbunov-Pinsker's nonanticipatory $ε-$entropy \cite{gorbunov-pinsker}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
