Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels

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The authors explore two 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 sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, they first derive the capacity of sampled analog channels for two prevalent sampling mechanisms: filtering followed by sampling and sampling following filter banks. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. Optimal pre-filters that maximize capacity are identified for both cases, as well as several kinds of channels for which these sampling mechanisms are optimal to maximize capacity at sub-Nyquist rates. They also highlight connections between sampled analog channel capacity and minimum mean squared error estimation from sampled data.