New Formulas of Ergodic Feedback Capacity of AGN Channels Driven by Stable and Unstable Autoregressive Noise

A Riccati-Lyapunov Approach to Nonfeedback Capacity of MIMO Gaussian Channels Driven by Stable and Unstable Noise

“…The main fundamental difference from previous characterizations of nonfeedback capacity found in the literature, i.e., [1]- [5], is that the consideration of nonergodic, time-varying and unstable noise, gives higher achievable rates compared to stable noise (see [13], [14], [16], [17]).…”

“…Sequential characterization of nonfeedback capacity for SISO AGN channels with general unstable noise with memory, are obtained in [14], and lower bounds in [15,Corollary II.1]. Additional lower bounds are discussed in [16], [17], which are equivalent to the Cover and Pombra [18] nonfeeback capacity formula. Equivalent characterizations of Cover and Pombra n−finite transmission, or block length for MIMO AGN channels with memory are presented in [19].…”

“…We emphasize that the consideration of unstable noise V n implies Y n is also unstable and therefore for our asymptotic analysis, we need to use the two innovations processes of V n and Y n , as in [13], [14], [16], [17], giving rise to the following characterization of C n (κ, P Y 1 ) ∈ [0, ∞] given by,…”

“…The solutions of the DREs and the Lyapunov equation are, Remark II.1. If the stabilizability condition is replaced by the unit circle controllability (see [22] for definition and [14]- [17] for specific examples), then Theorem II.4 and Theorem II.5 remain valid with the fundamental difference that all limits are not uniform for all P V 1 . For such a relaxation, the limits depend on P V 1 , Σ 1 , P 1 , Π 1 and the asymptotic optimization problem C ∞ (κ) may not be convex.…”