Strong data processing inequalities in power-constrained Gaussian channels
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) an...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2016
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| Online Access: | http://hdl.handle.net/1721.1/101004 https://orcid.org/0000-0003-2912-7972 https://orcid.org/0000-0002-2109-0979 |
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| author | Calmon, Flavio P. Polyanskiy, Yury Wu, Yihong |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Calmon, Flavio P. Polyanskiy, Yury Wu, Yihong |
| author_sort | Calmon, Flavio P. |
| collection | MIT |
| description | 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). |
| first_indexed | 2024-09-23T12:49:25Z |
| format | Article |
| id | mit-1721.1/101004 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:49:25Z |
| publishDate | 2016 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1010042022-10-01T11:21:19Z Strong data processing inequalities in power-constrained Gaussian channels Calmon, Flavio P. Polyanskiy, Yury Wu, Yihong Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Calmon, Flavio P. Polyanskiy, Yury 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). National Science Foundation (U.S.) (CAREER Award Grant CCF-12-53205) National Science Foundation (U.S.) (Grant IIS-1447879) National Science Foundation (U.S.). Center for Science of Information (Grant Agreement CCF-09-39370) 2016-01-27T17:26:39Z 2016-01-27T17:26:39Z 2015-06 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-7704-1 http://hdl.handle.net/1721.1/101004 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). https://orcid.org/0000-0003-2912-7972 https://orcid.org/0000-0002-2109-0979 en_US http://dx.doi.org/10.1109/ISIT.2015.7282918 Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Calmon, Flavio P. Polyanskiy, Yury Wu, Yihong Strong data processing inequalities in power-constrained Gaussian channels |
| title | Strong data processing inequalities in power-constrained Gaussian channels |
| title_full | Strong data processing inequalities in power-constrained Gaussian channels |
| title_fullStr | Strong data processing inequalities in power-constrained Gaussian channels |
| title_full_unstemmed | Strong data processing inequalities in power-constrained Gaussian channels |
| title_short | Strong data processing inequalities in power-constrained Gaussian channels |
| title_sort | strong data processing inequalities in power constrained gaussian channels |
| url | http://hdl.handle.net/1721.1/101004 https://orcid.org/0000-0003-2912-7972 https://orcid.org/0000-0002-2109-0979 |
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