  In the recent paper [1] it is shown, via an application example, that the
Cover and Pombra [2] "characterization of the $n-$block or transmission"
feedback capacity formula, of additive Gaussian noise (AGN) channels, is the
subject of much confusion in the literature, with redundant incorrect results.
The main objective of this paper is to clarify the main points of confusion and
remove any further ambiguity. The first part of the paper applies time-domain
methods, to derive for a first time, equivalent sequential characterizations of
the Cover and Pombra characterization of feedback capacity of AGN channels
driven by nonstationary and nonergodic Gaussian noise. 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 $n-$block capacity formula is expressed as a functional of two
generalized matrix difference Riccati equations (DRE) of filtering theory of
Gaussian systems, contrary to results that appeared in the literature. In the
second part of the paper the existence of the asymptotic limit of the $n-$block
feedback capacity formula is shown to be equivalent to the convergence
properties of solutions of the two generalized DREs. Further, necessary and or
sufficient conditions are identified for existence of the asymptotic limits,
for stable and unstable Gaussian noise, when the optimal input distributions
are time-invariant, but not necessarily stationary. The paper contains an in
depth analysis, with examples, of the specific technical issues, which are
overlooked in past literature [3-7], that studied the AGN channel of [2], for
stationary noises.
