Tree-structure Expectation Propagation for Decoding LDPC codes over Binary Erasure Channels

Expectation Propagation is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal distribution constraints in some check nodes of the LDPC Tanner graph. These additional constraints allow decoding the received codeword when the BP decoder gets stuck. In this paper, we first present the new decoding algorithm, whose complexity is identical to the BP decoder, and we then prove that it is able to decode codewords with a larger fraction of erasures, as the block size tends to infinity. The proposed algorithm can be also understood as a simplification of the Maxwell decoder, but without its computational complexity. We also illustrate that the new algorithm outperforms the BP decoder for finite block-siz

Digital communication receivers using Gaussian processes for machine learning

We propose Gaussian processes (GPs) as a novel nonlinear receiver for digital communication systems. The GPs framework can be used to solve both classification (GPC) and regression (GPR) problems. The minimum mean squared error solution is the expectation of the transmitted symbol given the information at the receiver, which is a nonlinear function of the received symbols for discrete inputs. GPR can be presented as a nonlinear MMSE estimator and thus capable of achieving optimal performance from MMSE viewpoint. Also, the design of digital communication receivers can be viewed as a detection problem, for which GPC is specially suited as it assigns posterior probabilities to each transmitted symbol. We explore the suitability of GPs as nonlinear digital communication receivers. GPs are Bayesian machine learning tools that formulates a likelihood function for its hyperparameters, which can then be set optimally. GPs outperform state-of-the-art nonlinear machine learning approaches that prespecify their hyperparameters or rely on cross validation. We illustrate the advantages of GPs as digital communication receivers for linear and nonlinear channel models for short training sequences and compare them to state-of-the-art nonlinear machine learning tools, such as support vector machines

Escherichia coli genes affecting recipient ability in plasmid conjugation: Are there any?

14 pages, 6 figures, 3 tables.[Background] How does the recipient cell contribute to bacterial conjugation? To answer this question we systematically analyzed the individual contribution of each Escherichia coli gene in matings using plasmid R388 as a conjugative plasmid. We used an automated conjugation assay and two sets of E. coli mutant collections: the Keio collection (3,908 E. coli single-gene deletion mutants) and a collection of 20,000 random mini-Tn10::Km insertion mutants in E. coli strain DH5α. The combined use of both collections assured that we screened > 99% of the E. coli non-essential genes in our survey.[Results] Results indicate that no non-essential recipient E. coli genes exist that play an essential role in conjugation. Mutations in the lipopolysaccharide (LPS) synthesis pathway had a modest effect on R388 plasmid transfer (6 – 32% of wild type). The same mutations showed a drastic inhibition effect on F-plasmid transfer, but only in liquid matings, suggesting that previously isolated conjugation-defective mutants do in fact impair mating pair formation in liquid mating, but not conjugative DNA processing or transport per se.[Conclusion] We conclude from our genome-wide screen that recipient bacterial cells cannot avoid being used as recipients in bacterial conjugation. This is relevant as an indication of the problems in curbing the dissemination of antibiotic resistance and suggests that conjugation acts as a pure drilling machine, with little regard to the constitution of the recipient cell.DPM was supported by a postdoctoral fellowship of Fundación Marqués de Valdecilla (IFIMAV), Spain. This work was financed by grants BFU2005-03477 from the Spanish Ministry of Education and Science, REIPI-RD06/0008 from the Ministry of Health and Consume, Instituto de Salud Carlos III – FEDER and EU 6th Framework Programme project SHM-CT-2005-019023 to FC.Peer reviewe

Aplicación del uso de RPA’S (drones) en la explotación de canteras y explotaciones a cielo abierto

Máster en Ingeniería de Caminos, Canales y Puerto

Extended Input Space Support Vector Machine

In some applications, the probability of error of a given classifier is too high for its practical application, but we are allowed to gather more independent test samples from the same class to reduce the probability of error of the final decision. From the point of view of hypothesis testing, the solution is given by the Neyman-Pearson lemma. However, there is no equivalent result to the Neyman-Pearson lemma when the likelihoods are unknown, and we are given a training dataset. In this brief, we explore two alternatives. First, we combine the soft (probabilistic) outputs of a given classifier to produce a consensus labeling for K test samples. In the second approach, we build a new classifier that directly computes the label for K test samples. For this second approach, we need to define an extended input space training set and incorporate the known symmetries in the classifier. This latter approach gives more accurate results, as it only requires an accurate classification boundary, while the former needs an accurate posterior probability estimate for the whole input space. We illustrate our results with well-known databases

Tree-Structure Expectation Propagation for LDPC Decoding over the BEC

We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). EP generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regime over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law (SL) for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization