Information regular and ψ-mixing channels

For channels with time structure we introduce a condition that characterizes infinite, asymptotically decreasing output memory called information regularity. We show that this condition is strictly weaker than asymptotic output-memorylessness, a property that was used to prove a coding theorem for continuous-time channels in case of infinite information capacity. We further show that the coding theorem still holds for information regular channels. We prove that Gaussian asymptotic output-memoryless channels have in fact finite output memory. This demonstrates that asymptotic output-memorylessness is quite restrictive. We consider discrete- and continuous-time channels with completely abstract alphabets in a unified framework and discuss practically relevant examples.