Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback
The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2013
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| Online Access: | http://hdl.handle.net/1721.1/81369 https://orcid.org/0000-0002-2109-0979 |
| _version_ | 1811090795339448320 |
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| author | Polyanskiy, Yury Poor, H. Vincent Verdu, Sergio |
| 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 Polyanskiy, Yury Poor, H. Vincent Verdu, Sergio |
| author_sort | Polyanskiy, Yury |
| collection | MIT |
| description | The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB below the noise level. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this nonasymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of -1.57 dB requires coding over at least k=10[superscript 6] information bits, while we construct a feedback scheme that transmits a single information bit with energy -1.59 dB and zero error. We also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop. |
| first_indexed | 2024-09-23T14:52:04Z |
| format | Article |
| id | mit-1721.1/81369 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:52:04Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/813692022-10-01T23:01:43Z Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback Polyanskiy, Yury Poor, H. Vincent Verdu, Sergio Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Polyanskiy, Yury Verdu, Sergio The minimum achievable energy per bit over memoryless Gaussian channels has been previously addressed in the limit when the number of information bits goes to infinity, in which case it is known that the availability of noiseless feedback does not lower the minimum energy per bit, which is -1.59 dB below the noise level. This paper analyzes the behavior of the minimum energy per bit for memoryless Gaussian channels as a function of k, the number of information bits. It is demonstrated that in this nonasymptotic regime, noiseless feedback leads to significantly better energy efficiency. In particular, without feedback achieving energy per bit of -1.57 dB requires coding over at least k=10[superscript 6] information bits, while we construct a feedback scheme that transmits a single information bit with energy -1.59 dB and zero error. We also show that unless k is very small, approaching the minimal energy per bit does not require using the feedback link except to signal that transmission should stop. National Science Foundation (U.S.) (Grant CCF-06-35154) National Science Foundation (U.S.) (grant CNS-09-05398) 2013-10-09T20:44:01Z 2013-10-09T20:44:01Z 2011-08 2011-05 Article http://purl.org/eprint/type/JournalArticle 0018-9448 1557-9654 http://hdl.handle.net/1721.1/81369 Polyanskiy, Yury, H. Vincent Poor, and Sergio Verdu. Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback. IEEE Transactions on Information Theory 57, no. 8 (August 2011): 4880-4902. https://orcid.org/0000-0002-2109-0979 en_US http://dx.doi.org/10.1109/TIT.2011.2159041 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers Polyanskiy via Amy Stout |
| spellingShingle | Polyanskiy, Yury Poor, H. Vincent Verdu, Sergio Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title | Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title_full | Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title_fullStr | Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title_full_unstemmed | Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title_short | Minimum Energy to Send k Bits Through the Gaussian Channel With and Without Feedback |
| title_sort | minimum energy to send k bits through the gaussian channel with and without feedback |
| url | http://hdl.handle.net/1721.1/81369 https://orcid.org/0000-0002-2109-0979 |
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