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Paris, France

Télécom ParisTech is one of the most selective grandes écoles in France. Located in Paris, it is also a member of prestigious ParisTech and Institut Telecom.It has established a school named Institut Eurécom in collaboration with EPFL at Sophia-Antipolis. Wikipedia.

Rioul O.,Telecom ParisTech
IEEE Transactions on Information Theory | Year: 2011

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 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. © 2006 IEEE. Source

Markham D.J.H.,Telecom ParisTech
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We give a highly intuitive geometric interpretation to entanglement via the Majorana representation, where these states correspond to points on a unit sphere. We use this to show how various entanglement properties are determined by the symmetry properties of the states. The geometric measure of entanglement is thus phrased entirely as a geometric optimization and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally, we see that different symmetries of the states correspond to different types of entanglement with respect to interconvertibility under stochastic local operations and classical communication. © 2011 American Physical Society. Source

Randriambololona H.,Telecom ParisTech
IEEE Transactions on Information Theory | Year: 2013

If C is a binary linear code, let C(2) be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for $C$ ranging in this family, C(2) also form an asymptotically good family. For this, we use algebraic-geometry codes, concatenation, and a fair amount of bilinear algebra. More precisely, the two main ingredients used in our construction are, first, a description of the symmetric square of an odd degree extension field in terms only of field operations of small degree, and second, a recent result of Garcia-Stichtenoth- Bassa-Beelen on the number of points of curves on such an odd degree extension field. © 1963-2012 IEEE. Source

A cryptography circuit, protected notably against information-leak observation attacks, comprises a functional key k

A method and apparatus are provided for modulating a binary source sequence including of a plurality of source words to generate modulated symbols. The method implements error-correction encoding of the plurality of source words, implementing one or more encoding modules, each implementing a separate error-correction code to generate a plurality of code words, the source words being encoded in series. The code words are interlaced to generate an interlaced sequence. The interlaced sequence is differentially modulated to generate modulated symbols. Each code word is broken down into at least one group with a number of bits equal to the base-2 logarithm of a number of states of a modulation implemented by the step of differentially modulating. The interlacing step distributes the groups such that two adjacent groups in the interlaced sequence belong to separate code words.

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