25 research outputs found

    Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

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    International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

    Bandwidth-efficient communication systems based on finite-length low density parity check codes

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    Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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    Correlation decay and decentralized optimization in graphical models

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    Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 213-229) and index.Many models of optimization, statistics, social organizations and machine learning capture local dependencies by means of a network that describes the interconnections and interactions of different components. However, in most cases, optimization or inference on these models is hard due to the dimensionality of the networks. This is so even when using algorithms that take advantage of the underlying graphical structure. Approximate methods are therefore needed. The aim of this thesis is to study such large-scale systems, focusing on the question of how randomness affects the complexity of optimizing in a graph; of particular interest is the study of a phenomenon known as correlation decay, namely, the phenomenon where the influence of a node on another node of the network decreases quickly as the distance between them grows. In the first part of this thesis, we develop a new message-passing algorithm for optimization in graphical models. We formally prove a connection between the correlation decay property and (i) the near-optimality of this algorithm, as well as (ii) the decentralized nature of optimal solutions. In the context of discrete optimization with random costs, we develop a technique for establishing that a system exhibits correlation decay. We illustrate the applicability of the method by giving concrete results for the cases of uniform and Gaussian distributed cost coefficients in networks with bounded connectivity. In the second part, we pursue similar questions in a combinatorial optimization setting: we consider the problem of finding a maximum weight independent set in a bounded degree graph, when the node weights are i.i.d. random variables.(cont.) Surprisingly, we discover that the problem becomes tractable for certain distributions. Specifically, we construct a PTAS for the case of exponentially distributed weights and arbitrary graphs with degree at most 3, and obtain generalizations for higher degrees and different distributions. At the same time we prove that no PTAS exists for the case of exponentially distributed weights for graphs with sufficiently large but bounded degree, unless P=NP. Next, we shift our focus to graphical games, which are a game-theoretic analog of graphical models. We establish a connection between the problem of finding an approximate Nash equilibrium in a graphical game and the problem of optimization in graphical models. We use this connection to re-derive NashProp, a message-passing algorithm which computes Nash equilibria for graphical games on trees; we also suggest several new search algorithms for graphical games in general networks. Finally, we propose a definition of correlation decay in graphical games, and establish that the property holds in a restricted family of graphical games. The last part of the thesis is devoted to a particular application of graphical models and message-passing algorithms to the problem of early prediction of Alzheimer's disease. To this end, we develop a new measure of synchronicity between different parts of the brain, and apply it to electroencephalogram data. We show that the resulting prediction method outperforms a vast number of other EEG-based measures in the task of predicting the onset of Alzheimer's disease.by Théophane Weber.Ph.D
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