Shannon meets Nyquist: the tradeoff between capacity and sub-Nyquist sampling
The capacity of communication channels has largely been studied in the discrete-time domain, under the premise that sampling, if done above the Nyquist rate of the channel bandwidth, preserves information. However, hardware and power limitations often preclude sampling at this rate, especially for wideband channels. This gives rise to 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; what is the optimal sub-Nyquist rate sampling strategy to maximize capacity for both time-invariant and time-varying channels. In this talk, we will explore these fundamental questions and provide some preliminary answers about fundamental tradeoffs between sampling and capacity. In particular, we will discuss the optimal sampling mechanism for an LTI Gaussian channel, and the optimal universal (channel-independent) sampling method that minimizes the information loss for a compound multiband channel.