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
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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 -