On the dispersions of three network information theory problems

Vincent Y.F. Tan, Oliver Kosut

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

We characterize fundamental limits for the Slepian-Wolf problem, the multiple-access channel and the asymmetric broadcast channel in the finite blocklength setting. For the Slepian-Wolf problem (distributed lossless source coding), we introduce a fundamental quantity known as the entropy dispersion matrix. We show that if this matrix is positive-definite, the optimal rate region under the constraint of a fixed blocklength and non-zero error probability has a curved boundary compared to being polyhedral for the asymptotic Slepian-Wolf scenario. In addition, the entropy dispersion matrix governs the rate of convergence of the non-asymptotic region to the asymptotic one. We develop a general universal achievability procedure for finite blocklength analyses of other network information theory problems such as the multiple-access channel and broadcast channel. We provide inner bounds to these problems using a key result known as the vector rate redundancy theorem which is proved using a multidimensional version of the Berry-Essèen theorem. We show that a so-called information dispersion matrix characterizes these inner bounds.

Original languageEnglish (US)
Title of host publication2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
DOIs
StatePublished - Nov 12 2012
Externally publishedYes
Event2012 46th Annual Conference on Information Sciences and Systems, CISS 2012 - Princeton, NJ, United States
Duration: Mar 21 2012Mar 23 2012

Publication series

Name2012 46th Annual Conference on Information Sciences and Systems, CISS 2012

Other

Other2012 46th Annual Conference on Information Sciences and Systems, CISS 2012
CountryUnited States
CityPrinceton, NJ
Period3/21/123/23/12

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Keywords

  • Dispersion
  • Finite blocklength
  • Network information theory

ASJC Scopus subject areas

  • Information Systems

Cite this

Tan, V. Y. F., & Kosut, O. (2012). On the dispersions of three network information theory problems. In 2012 46th Annual Conference on Information Sciences and Systems, CISS 2012 [6310768] (2012 46th Annual Conference on Information Sciences and Systems, CISS 2012). https://doi.org/10.1109/CISS.2012.6310768