Relative entropy at the channel output of a capacity-achieving code
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optcodes_allerton.pdf
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155.68 KB
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Author(s)
Polyanskiy, Yury
Verdu, Sergio
Date Issued
September 2011
Journal
Proceedings of the 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Polyanskiy, Yury, and Sergio Verdu. Relative Entropy at the Channel Output of a Capacity-achieving Code. In 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 52-59. Institute of Electrical and Electronics Engineers, 2011.
Version
Author's final manuscript
Abstract
In this paper we establish a new inequality tying together the coding rate, the probability of error and the relative entropy between the channel and the auxiliary output distribution. This inequality is then used to show the strong converse, and to prove that the output distribution of a code must be close, in relative entropy, to the capacity achieving output distribution (for DMC and AWGN). One of the key tools in our analysis is the concentration of measure (isoperimetry).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/Allerton.2011.6120149
