Shannon meets Nyquist: The interplay between capacity and sampling

We explore several fundamental questions at the intersection of sampling theory and information theory: how is channel capacity affected by sampling below the channel´s Nyquist rate, and what is the optimal input and sampling strategy at a given sub-Nyquist sampling rate. In particular, we derive the capacity of sampled analog channels for several sampling mechanisms, including a filter followed by sampling and a filter bank followed by sampling. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. These results demonstrate the tradeoff between channel capacity and sampling rate, and also illustrate the interplay between sampling techniques and capacity of sampled analog channels.