  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.
