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When is Shannon’s lower bound tight at finite blocklength?

Kostina, Victoria (2016) When is Shannon’s lower bound tight at finite blocklength? In: 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016. IEEE , Piscataway, NJ, pp. 982-989. ISBN 978-1-5090-4551-8. http://resolver.caltech.edu/CaltechAUTHORS:20170221-071301966

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Abstract

This paper formulates an abstract version of Shannon's lower bound that applies to abstract sources and arbitrary distortion measures and that recovers the classical Shannon lower bound as a special case. A necessary and sufficient condition for it to be attained exactly is presented. It is demonstrated that whenever that condition is met, the d-tilted information of the source adopts a simple, explicit representation that parallels Shannon's lower bound. That convenient representation simplifies the non-asymptotic analysis of achievable rate-distortion tradeoffs. In particular, if a memoryless source meets Shannon's lower bound with equality, then its rate-dispersion function is given simply by the varentropy of the source.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ALLERTON.2016.7852341DOIArticle
http://ieeexplore.ieee.org/document/7852341/PublisherArticle
ORCID:
AuthorORCID
Kostina, Victoria0000-0002-2406-7440
Additional Information:© 2016 IEEE. Date of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. This work was supported in part by the National Science Foundation (NSF) under Grant CCF-1566567, and by the Simons Institute for the Theory of Computing.
Funders:
Funding AgencyGrant Number
NSFCCF-1566567
Simons Institute for the Theory of ComputingUNSPECIFIED
Subject Keywords:Lossy source coding, rate-distortion function Shannon's lower bound, finite blocklength regime, dispersion
Record Number:CaltechAUTHORS:20170221-071301966
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170221-071301966
Official Citation:V. Kostina, "When is Shannon's lower bound tight at finite blocklength?," 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 2016, pp. 982-989. doi: 10.1109/ALLERTON.2016.7852341
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74417
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Feb 2017 17:51
Last Modified:21 Feb 2017 17:51

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