Strong data processing inequalities in power-constrained Gaussian channels
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Polyanskiy_Strong data.pdf
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169.27 KB
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Author(s)
Calmon, Flavio P.
Polyanskiy, Yury
Wu, Yihong
Date Issued
June 2015
Journal
Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Calmon, Flavio P., Yury Polyanskiy, and Yihong Wu. “Strong Data Processing Inequalities in Power-Constrained Gaussian Channels.” 2015 IEEE International Symposium on Information Theory (ISIT) (June 2015).
Version
Author's final manuscript
Abstract
This work presents strong data processing results for the power-constrained additive Gaussian channel. Explicit bounds on the amount of decrease of mutual information under convolution with Gaussian noise are shown. The analysis leverages the connection between information and estimation (I-MMSE) and the following estimation-theoretic result of independent interest. It is proved that any random variable for which there exists an almost optimal (in terms of the mean-squared error) linear estimator operating on the Gaussian-corrupted measurement must necessarily be almost Gaussian (in terms of the Kolmogorov-Smirnov distance).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/ISIT.2015.7282918
