80 research outputs found
Information Theoretic Proofs of Entropy Power Inequalities
While most useful information theoretic inequalities can be deduced from the
basic properties of entropy or mutual information, up to now Shannon's entropy
power inequality (EPI) is an exception: Existing information theoretic proofs
of the EPI hinge on representations of differential entropy using either Fisher
information or minimum mean-square error (MMSE), which are derived from de
Bruijn's identity. In this paper, we first present an unified view of these
proofs, showing that they share two essential ingredients: 1) a data processing
argument applied to a covariance-preserving linear transformation; 2) an
integration over a path of a continuous Gaussian perturbation. Using these
ingredients, we develop a new and brief proof of the EPI through a mutual
information inequality, which replaces Stam and Blachman's Fisher information
inequality (FII) and an inequality for MMSE by Guo, Shamai and Verd\'u used in
earlier proofs. The result has the advantage of being very simple in that it
relies only on the basic properties of mutual information. These ideas are then
generalized to various extended versions of the EPI: Zamir and Feder's
generalized EPI for linear transformations of the random variables, Takano and
Johnson's EPI for dependent variables, Liu and Viswanath's
covariance-constrained EPI, and Costa's concavity inequality for the entropy
power.Comment: submitted for publication in the IEEE Transactions on Information
Theory, revised versio
Brascamp-Lieb Inequality and Its Reverse: An Information Theoretic View
We generalize a result by Carlen and Cordero-Erausquin on the equivalence
between the Brascamp-Lieb inequality and the subadditivity of relative entropy
by allowing for random transformations (a broadcast channel). This leads to a
unified perspective on several functional inequalities that have been gaining
popularity in the context of proving impossibility results. We demonstrate that
the information theoretic dual of the Brascamp-Lieb inequality is a convenient
setting for proving properties such as data processing, tensorization,
convexity and Gaussian optimality. Consequences of the latter include an
extension of the Brascamp-Lieb inequality allowing for Gaussian random
transformations, the determination of the multivariate Wyner common information
for Gaussian sources, and a multivariate version of Nelson's hypercontractivity
theorem. Finally we present an information theoretic characterization of a
reverse Brascamp-Lieb inequality involving a random transformation (a multiple
access channel).Comment: 5 pages; to be presented at ISIT 201
Gaussian Secure Source Coding and Wyner's Common Information
We study secure source-coding with causal disclosure, under the Gaussian
distribution. The optimality of Gaussian auxiliary random variables is shown in
various scenarios. We explicitly characterize the tradeoff between the rates of
communication and secret key. This tradeoff is the result of a mutual
information optimization under Markov constraints. As a corollary, we deduce a
general formula for Wyner's Common Information in the Gaussian setting.Comment: ISIT 2015, 5 pages, uses IEEEtran.cl
Secure Multiterminal Source Coding with Side Information at the Eavesdropper
The problem of secure multiterminal source coding with side information at
the eavesdropper is investigated. This scenario consists of a main encoder
(referred to as Alice) that wishes to compress a single source but
simultaneously satisfying the desired requirements on the distortion level at a
legitimate receiver (referred to as Bob) and the equivocation rate --average
uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed
the presence of a (public) rate-limited link between Alice and Bob. In this
setting, Eve perfectly observes the information bits sent by Alice to Bob and
has also access to a correlated source which can be used as side information. A
second encoder (referred to as Charlie) helps Bob in estimating Alice's source
by sending a compressed version of its own correlated observation via a
(private) rate-limited link, which is only observed by Bob. For instance, the
problem at hands can be seen as the unification between the Berger-Tung and the
secure source coding setups. Inner and outer bounds on the so called
rates-distortion-equivocation region are derived. The inner region turns to be
tight for two cases: (i) uncoded side information at Bob and (ii) lossless
reconstruction of both sources at Bob --secure distributed lossless
compression. Application examples to secure lossy source coding of Gaussian and
binary sources in the presence of Gaussian and binary/ternary (resp.) side
informations are also considered. Optimal coding schemes are characterized for
some cases of interest where the statistical differences between the side
information at the decoders and the presence of a non-zero distortion at Bob
can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table
A Note on the Secrecy Capacity of the Multi-antenna Wiretap Channel
Recently, the secrecy capacity of the multi-antenna wiretap channel was
characterized by Khisti and Wornell [1] using a Sato-like argument. This note
presents an alternative characterization using a channel enhancement argument.
This characterization relies on an extremal entropy inequality recently proved
in the context of multi-antenna broadcast channels, and is directly built on
the physical intuition regarding to the optimal transmission strategy in this
communication scenario.Comment: 10 pages, 0 figure
A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities
This paper proposes a unifying variational approach for proving and extending
some fundamental information theoretic inequalities. Fundamental information
theory results such as maximization of differential entropy, minimization of
Fisher information (Cram\'er-Rao inequality), worst additive noise lemma,
entropy power inequality (EPI), and extremal entropy inequality (EEI) are
interpreted as functional problems and proved within the framework of calculus
of variations. Several applications and possible extensions of the proposed
results are briefly mentioned
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