Shannon meets Nyquist: The interplay between capacity and sampling

Yuxin Chen; Andrea J. Goldsmith; Yonina C. Eldar

doi:10.1109/Allerton.2011.6120289

Shannon meets Nyquist: The interplay between capacity and sampling

Yuxin Chen
, Andrea J. Goldsmith
, Yonina C. Eldar

Stony Brook University

Stony Brook University

Stanford University
Technion-Israel Institute of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Title of host publication	2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages	1090-1097
Number of pages	8
DOIs	https://doi.org/10.1109/Allerton.2011.6120289
State	Published - 2011
Event	2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States Duration: Sep 28 2011 → Sep 30 2011

Publication series

Name	2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Conference

Conference	2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Country/Territory	United States
City	Monticello, IL
Period	09/28/11 → 09/30/11

Keywords

channel capacity
sampled analog channels
sub-Nyquist sampling

Access to Document

10.1109/Allerton.2011.6120289

Cite this

Chen, Y., Goldsmith, A. J., & Eldar, Y. C. (2011). Shannon meets Nyquist: The interplay between capacity and sampling. In 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 (pp. 1090-1097). Article 6120289 (2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011). https://doi.org/10.1109/Allerton.2011.6120289

@inproceedings{3418fcd97893406f896182620bd72ad5,

title = "Shannon meets Nyquist: The interplay between capacity and sampling",

abstract = "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.",

keywords = "channel capacity, sampled analog channels, sub-Nyquist sampling",

author = "Yuxin Chen and Goldsmith, \{Andrea J.\} and Eldar, \{Yonina C.\}",

year = "2011",

doi = "10.1109/Allerton.2011.6120289",

language = "English",

isbn = "9781457718168",

series = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011",

pages = "1090--1097",

booktitle = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011",

note = "2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 ; Conference date: 28-09-2011 Through 30-09-2011",

}

Chen, Y, Goldsmith, AJ & Eldar, YC 2011, Shannon meets Nyquist: The interplay between capacity and sampling. in 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011., 6120289, 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011, pp. 1090-1097, 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011, Monticello, IL, United States, 09/28/11. https://doi.org/10.1109/Allerton.2011.6120289

Shannon meets Nyquist: The interplay between capacity and sampling. / Chen, Yuxin; Goldsmith, Andrea J.; Eldar, Yonina C.
2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011. 2011. p. 1090-1097 6120289 (2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Y1 - 2011

N2 - 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.

AB - 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.

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KW - sub-Nyquist sampling

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DO - 10.1109/Allerton.2011.6120289

M3 - Conference contribution

SN - 9781457718168

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SP - 1090

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BT - 2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Y2 - 28 September 2011 through 30 September 2011

ER -

Shannon meets Nyquist: The interplay between capacity and sampling

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Keywords

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