On Sampling Continuous-Time AWGN Channels

For a continuous-Time additive white Gaussian noise (AWGN) channel with possible feedback, it has been shown that as sampling gets infinitesimally fine, the mutual information of the associative discrete-Time channels converges to that of the original continuous-Time channel. We give in this paper more quantitative strengthenings of this result, which, among other implications, characterize how over-sampling approaches the true mutual information of a continuous-Time Gaussian channel with bandwidth limit. The assumptions in our results are relatively mild. In particular, for the non-feedback case, compared to the Shannon-Nyquist sampling theorem, a widely used tool to connect continuous-Time Gaussian channels to their discrete-Time counterparts that requires the band-limitedness of the channel input, our results only require some integrability conditions on the power spectral density function of the input.