Empirical processes and typical sequences

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


This paper proposes a new notion of a typical sequence over an abstract alphabet based on approximation of memoryless sources by empirical distributions, uniformly over a class of measurable "test functions." In the finite-alphabet case, we can take all uniformly bounded functions and recover the usual notion of typicality under total variation distance. For a general alphabet, this function class is too large, and must be restricted. We develop our notion of typicality with respect to any Glivenko-Cantelli function class (which admits a Uniform Law of Large Numbers) and demonstrate its power by deriving fundamental limits on achievable rates in several settings that can be reduced to uniform approximation of general-alphabet memoryless sources with respect to a suitable function class.

Original languageEnglish (US)
Title of host publication2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
Number of pages5
StatePublished - Aug 23 2010
Externally publishedYes
Event2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States
Duration: Jun 13 2010Jun 18 2010

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8103


Other2010 IEEE International Symposium on Information Theory, ISIT 2010
CountryUnited States
CityAustin, TX

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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