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Error Rates of Capacity-Achieving Codes Are Convex

Loyka, Sergey and Gagnon, François and Kostina, Victoria (2010) Error Rates of Capacity-Achieving Codes Are Convex. In: 2010 IEEE International Symposium on Information Theory. IEEE International Symposium on Information Theory . IEEE , Piscataway, NJ, pp. 325-329. ISBN 978-1-4244-7890-3. http://resolver.caltech.edu/CaltechAUTHORS:20140910-094918979

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Abstract

Motivated by a wide-spread use of convex optimization techniques, convexity properties of bit error rate of the maximum likelihood detector operating in the AWGN channel are studied for arbitrary constellations and bit mappings, which also includes coding under maximum-likelihood decoding. Under this generic setting, the pairwise probability of error and bit error rate are shown to be convex functions of the SNR and noise power in the high SNR/low noise regime with explicitly-determined boundary. Any code, including capacity-achieving ones, whose decision regions include the hardened noise spheres (from the noise sphere hardening argument in the channel coding theorem) satisfies this high SNR requirement and thus has convex error rates in both SNR and noise power. We conjecture that all capacity-achieving codes have convex error rates.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2010.5513337DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5513337PublisherArticle
http://arxiv.org/abs/1004.2683arXivArticle
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2010 Crown.
Record Number:CaltechAUTHORS:20140910-094918979
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140910-094918979
Official Citation:Loyka, S.; Gagnon, F.; Kostina, V., "Error rates of capacity-achieving codes are convex," Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on , vol., no., pp.325,329, 13-18 June 2010 doi: 10.1109/ISIT.2010.5513337
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49528
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Sep 2014 19:51
Last Modified:07 Sep 2017 00:06

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