TY - GEN

T1 - Empirical processes and typical sequences

AU - Raginsky, Maxim

PY - 2010/8/23

Y1 - 2010/8/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77955668765&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955668765&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2010.5513601

DO - 10.1109/ISIT.2010.5513601

M3 - Conference contribution

AN - SCOPUS:77955668765

SN - 9781424469604

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1458

EP - 1462

BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010

Y2 - 13 June 2010 through 18 June 2010

ER -