The main objective of this paper is to derive a new sequential characterization of the Cover and Pombra \cite{cover-pombra1989} characterization of the $n-$finite block or transmission feedback information ($n$-FTFI) capacity, which clarifies several issues of confusion and incorrect interpretation of results in literature. The optimal channel input processes of the new equivalent sequential characterizations are expressed as functionals of a sufficient statistic and a Gaussian orthogonal innovations process. From the new representations follows that the Cover and Pombra characterization of the $n-$FTFI capacity is expressed as a functional of two generalized matrix difference Riccati equations (DRE) of filtering theory of Gaussian systems. This contradicts results which are redundant in the literature, and illustrates the fundamental complexity of the feedback capacity formula.

中文翻译：

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关于封面和 Pombra 高斯反馈能力：通过足够的统计量完成序列特征

本文的主要目的是推导出一个新的序列表征的 Cover 和 Pombra \cite{cover-pombra1989} 表征 $n-$finite 块或传输反馈信息 ($n$-FTFI) 容量，它阐明了几个文献中结果的混淆和错误解释问题。新等效序列特征的最优通道输入过程被表示为充分统计和高斯正交创新过程的泛函。根据新的表示，$n-$FTFI 容量的 Cover 和 Pombra 表征被表示为高斯系统滤波理论的两个广义矩阵差分 Riccati 方程 (DRE) 的函数。这与文献中多余的结果相矛盾，