44 research outputs found
Empirical processes, typical sequences and coordinated actions in standard Borel spaces
This paper proposes a new notion of typical sequences on a wide class of
abstract alphabets (so-called standard Borel spaces), which is based on
approximations 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 strong
typicality (or typicality under the total variation distance). For a general
alphabet, however, this function class turns out to be too large, and must be
restricted. With this in mind, we define typicality with respect to any
Glivenko-Cantelli function class (i.e., a function class that admits a Uniform
Law of Large Numbers) and demonstrate its power by giving simple derivations of
the fundamental limits on the achievable rates in several source coding
scenarios, in which the relevant operational criteria pertain to reproducing
empirical averages of a general-alphabet stationary memoryless source with
respect to a suitable function class.Comment: 14 pages, 3 pdf figures; accepted to IEEE Transactions on Information
Theor
Secret Key Agreement: General Capacity and Second-Order Asymptotics
We revisit the problem of secret key agreement using interactive public
communication for two parties and propose a new secret key agreement protocol.
The protocol attains the secret key capacity for general observations and
attains the second-order asymptotic term in the maximum length of a secret key
for independent and identically distributed observations. In contrast to the
previously suggested secret key agreement protocols, the proposed protocol uses
interactive communication. In fact, the standard one-way communication protocol
used prior to this work fails to attain the asymptotic results above. Our
converse proofs rely on a recently established upper bound for secret key
lengths. Both our lower and upper bounds are derived in a single-shot setup and
the asymptotic results are obtained as corollaries