MIMO two-way X relay channel, and L-cluster MIMO multiway relay channel. Previous studies mainly considered the achievability of the DoF cut-set bound 2N at the antenna configuration N < 2M by applying signal alignment for network coding. This work aims to investigate the achievability of the Do

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The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sam-pling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement

Abstract not found

A particularly important sector for the stability of financial systems is the banking sector. Banks play a central role in the money creation process and in the payment system. Moreover, bank credit is an important factor in the financing of investment and growth. Faltering banking systems have

de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury:

We explore two fundamental questions at the intersection of sampling theory and information theory: how is channel capacity affected by sampling below the channel’s Nyquist rate, and what sub-Nyquist sampling strategy should be employed to maximize capacity. In particular, we first derive the capacity of sampled analog channels for two prevalent sampling mechanisms: filtering followed by sampling and sampling following filter banks. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. Optimal prefilters that maximize capacity are identified for both cases, as well as several kinds of channels for which these sampling mechanisms are optimal to maximize capacity at sub-Nyquist rates. We also highlight connections between sampled analog channel capacity and minimum mean squared error estimation from sampled data. In particular, it is shown that for both filtering and filter-bank sampling strategies, the filters maximizing capacity and minimizing mean squared error are equivalent. We also investigate a more general sampling strategy by adding modulation banks to filter-bank sampling. This general sampling method subsumes most nonuniform sampling techniques applied in both theory and practice. We also show a connection between this general sampling method and MIMO Gaussian channels. We then identify the optimal sampling strategy for piece-wise flat sampled

mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

Caractérisation des problèmes conjoints de détection et d'estimation

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte