On Sampling Continuous-Time AWGN Channels

Guangyue Han; Shlomo Shamai

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arXiv · 2002.02716

On Sampling Continuous-Time AWGN Channels

Guangyue Han·Shlomo Shamai

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Abstract

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.

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Guangyue Han, Shlomo Shamai. 2020-08-23. On Sampling Continuous-Time AWGN Channels. https://arxiv.org/abs/2002.02716

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