  In this paper it is shown that the nonfeedback capacity of multiple-input
multiple-output (MIMO) additive Gaussian noise (AGN) channels, when the noise
is nonstationary and unstable, is characterized by an asymptotic optimization
problem that involves, a generalized matrix algebraic Riccati equation (ARE) of
filtering theory, and a matrix Lyapunov equation of stability theory of
Gaussian systems. Furthermore, conditions are identified such that, the
characterization of nonfeedback capacity corresponds to the uniform asymptotic
per unit time limit, over all initial distributions, of the characterization of
a finite block or transmission without feedback information (FTwFI) capacity,
which involves, two generalized matrix difference Riccati equations (DREs) and
a matrix difference Lyapunov equation.
