From Feedback Capacity to Tight Achievable Rates without Feedback for AGN Channels with 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]).…”

“…Bounds on nonfeedback capacity for single-input single-output (SISO) AGN channel with stable noise with memory, are derived in [10]- [12], as well as comparisons to feedback capacity. Recently, sequential time-domain characterizations of nonfeedback capacity for SISO AGN channels with unstable, finite-memory autoregressive noise are presented in [13]. 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].…”

“…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,…”