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Abstract—A coding scheme for the two-receivers Gaussian broadcast channel (BC) with feedback is proposed. For some asymmetric settings it achieves new rate pairs. Moreover, it achieves prelog 2 when the noises at the two receivers are fully positively correlated and of unequal variances, thus

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Abstract — We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterization of the RKHS associated with the SLGM, we derive a lower bound on the minimum variance achievable by estimators with a prescribed bias function, including the important special case of unbiased estimation. This bound is obtained via an orthogonal projection of the prescribed mean function onto a subspace of the RKHS associated with the SLGM. It provides an approximation to the minimum achievable variance (Barankin bound) that is tighter than any known bound. Our bound holds for an arbitrary system matrix, including the overdetermined and underdetermined cases. We specialize

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Caractérisation des problèmes conjoints de détection et d'estimation

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We study the generalizations of the well-known Lieb-Thirring inequality for the mag-netic Schrodinger operator with nonconstant magnetic eld. Our main result is the natu-rally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic elds (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which eectively estimates the oscillatory eect due to the magnetic phase