164,272 research outputs found
Minimum Rates of Approximate Sufficient Statistics
Given a sufficient statistic for a parametric family of distributions, one
can estimate the parameter without access to the data. However, the memory or
code size for storing the sufficient statistic may nonetheless still be
prohibitive. Indeed, for independent samples drawn from a -nomial
distribution with degrees of freedom, the length of the code scales as
. In many applications, we may not have a useful notion of
sufficient statistics (e.g., when the parametric family is not an exponential
family) and we also may not need to reconstruct the generating distribution
exactly. By adopting a Shannon-theoretic approach in which we allow a small
error in estimating the generating distribution, we construct various {\em
approximate sufficient statistics} and show that the code length can be reduced
to . We consider errors measured according to the
relative entropy and variational distance criteria. For the code constructions,
we leverage Rissanen's minimum description length principle, which yields a
non-vanishing error measured according to the relative entropy. For the
converse parts, we use Clarke and Barron's formula for the relative entropy of
a parametrized distribution and the corresponding mixture distribution.
However, this method only yields a weak converse for the variational distance.
We develop new techniques to achieve vanishing errors and we also prove strong
converses. The latter means that even if the code is allowed to have a
non-vanishing error, its length must still be at least .Comment: To appear in the IEEE Transactions on Information Theor
Finite-Block-Length Analysis in Classical and Quantum Information Theory
Coding technology is used in several information processing tasks. In
particular, when noise during transmission disturbs communications, coding
technology is employed to protect the information. However, there are two types
of coding technology: coding in classical information theory and coding in
quantum information theory. Although the physical media used to transmit
information ultimately obey quantum mechanics, we need to choose the type of
coding depending on the kind of information device, classical or quantum, that
is being used. In both branches of information theory, there are many elegant
theoretical results under the ideal assumption that an infinitely large system
is available. In a realistic situation, we need to account for finite size
effects. The present paper reviews finite size effects in classical and quantum
information theory with respect to various topics, including applied aspects
Variable-Length Coding with Cost Allowing Non-Vanishing Error Probability
We derive a general formula of the minimum achievable rate for
fixed-to-variable length coding with a regular cost function by allowing the
error probability up to a constant . For a fixed-to-variable
length code, we call the set of source sequences that can be decoded without
error the dominant set of source sequences. For any two regular cost functions,
it is revealed that the dominant set of source sequences for a code attaining
the minimum achievable rate with a cost function is also the dominant set for a
code attaining the minimum achievable rate with the other cost function. We
also give a general formula of the second-order minimum achievable rate.Comment: 7 pages; extended version of a paper accepted by ISITA201
Broadcast Capacity Region of Two-Phase Bidirectional Relaying
In a three-node network a half-duplex relay node enables bidirectional
communication between two nodes with a spectral efficient two phase protocol.
In the first phase, two nodes transmit their message to the relay node, which
decodes the messages and broadcast a re-encoded composition in the second
phase. In this work we determine the capacity region of the broadcast phase. In
this scenario each receiving node has perfect information about the message
that is intended for the other node. The resulting set of achievable rates of
the two-phase bidirectional relaying includes the region which can be achieved
by applying XOR on the decoded messages at the relay node. We also prove the
strong converse for the maximum error probability and show that this implies
that the [\eps_1,\eps_2]-capacity region defined with respect to the average
error probability is constant for small values of error parameters \eps_1,
\eps_2.Comment: 25 pages, 2 figures, submitted to IEEE Transactions on Information
Theor
Strongly Secure Privacy Amplification Cannot Be Obtained by Encoder of Slepian-Wolf Code
The privacy amplification is a technique to distill a secret key from a
random variable by a function so that the distilled key and eavesdropper's
random variable are statistically independent. There are three kinds of
security criteria for the key distilled by the privacy amplification: the
normalized divergence criterion, which is also known as the weak security
criterion, the variational distance criterion, and the divergence criterion,
which is also known as the strong security criterion. As a technique to distill
a secret key, it is known that the encoder of a Slepian-Wolf (the source coding
with full side-information at the decoder) code can be used as a function for
the privacy amplification if we employ the weak security criterion. In this
paper, we show that the encoder of a Slepian-Wolf code cannot be used as a
function for the privacy amplification if we employ the criteria other than the
weak one.Comment: 10 pages, no figure, A part of this paper will be presented at 2009
IEEE International Symposium on Information Theory in Seoul, Korea. Version 2
is a published version. The results are not changed from version 1.
Explanations are polished and some references are added. In version 3, only
style and DOI are edite
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