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Information-Theoretic Extensions of the Shannon-Nyquist Sampling Theorem

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MQIW05 - Beyond I.I.D. in information theory

This talk will present information-theoretic extensions of the classical Shannon-Nyquist sampling theorem and some of their applications. More specifically, we consider a continuous-time white Gaussian channel, which is typically formulated using a white Gaussian noise. A conventional way for examining such a channel is the sampling approach based on the Shannon-Nyquist sampling theorem, where the original continuous-time channel is converted to an equivalent discrete-time channel, to which a great variety of established tools and methodology can be applied. However, one of the key issues of this scheme is that continuous-time feedback and memory cannot be incorporated into the channel model. It turns out that this issue can be circumvented by considering the Brownian motion formulation of a continuous-time white Gaussian channel. Nevertheless, as opposed to the white Gaussian noise formulation, a link that establishes the information-theoretic connection between a continuous -time channel under the Brownian motion formulation and its discrete-time counterparts has long been missing. This paper is to fill this gap by establishing causality-preserving connections between continuous-time Gaussian feedback/memory channels and their associated discrete-time versions in the forms of sampling and approximation theorems, which we believe will help to contribute the further development of continuous-time information theory.

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