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

Monitoring of the water particle velocity field near the seabed under different wave and tidal scenarios: a real case

Monitoring of water particle velocity on the sea bed is crucial to study morphological shore changes in a coast at intermediate and shallow water depth under progressive surface waves and tidal flow current. Therefore, 3-D particle velocity was monitored continuously at the bottom of Santa Maria del Mar (SMM) beach (SW Spain) by means of a single point current meter during 3 weeks in 2007 since August 28. The current meter was placed at 0.45m above the seabed in order to acquire instantaneous velocity. Wave properties (height and period) were taken from the nearby wave buoy and tidal data were taken from a tidal gauge station. Wave-induced bottom particle velocities were obtained during spring and neap tides at a d/L (depth over wave length) parameter ranging from 0.06 to 0.3. Bottom water particle velocity near the seabed ranges from 0 to ± 0.5 m/sec of which about 82% does not exceed 0.2 m/sec during monitoring. Therefore, only 18% of the surveyed water particle velocities exceed the critical Shield parameter of the beach sand (d50 = 0.23mm) which is about 0.05-0.2 depending on Reynolds number. Results show that maximum horizontal speed is obviously lower during the slack tide (high or low tide) in comparison with flood tide and ebb tide. Moreover, speed is higher during ebb tide in comparison to adjacent flood tide, with steady wave climate. Finally and among other conclusions, the maximum real values of the bottom current surveyed in SMM, as well as the Shield parameter, substantially coincide with the theoretical estimates calculated for a given wave and tidal climate

Automatic classification system of Raman spectra applied to pigments analysis

Raman spectroscopy is one of the few non-destructive techniques capable of identifying pigments in art works. Raman spectra contain powerful information that can be used to identify unknown compounds and their chemical structures. However, the analysis of spectral data comes with some difficulties, and therefore the spectral interpretation is not straightforward. Sometimes, there are very little differences in the spectral data concerning to specific identification objectives, for instance, in polymorphic discrimination or in the discrimination of natural and synthetic forms of certain pigments. Moreover, this discrimination is often performed manually so that the process can be repetitive, subjective and particularly time-consuming. The result is an increasing motivation to automate the identification process involved in the classification of pigments in paint. In this paper, we propose a system to automatically classify the spectral data into specific and well-known classes, i.e. reference classes. The proposal is based on a combination of chemometric techniques, which provides a powerful way to achieve spectral separability so that it is possible to discriminate between very similar spectra in an automatic way. In this regard, a decision-making algorithm was specifically developed to select the corresponding reference class with no user input, which was successfully validated using simulated spectra. The implemented methodology was used to classify Raman spectra of pigments commonly present in artist's paints in experimental cases, providing reliable and consistent results. Therefore, the presented system can play a good auxiliary role in the analysts' endpoint classification.Peer ReviewedPostprint (author's final draft

Image encryption system based on a nonlinear joint transform correlator for the simultaneous authentication of two users

We propose a new encryption system based on a nonlinear joint transform correlator (JTC) using the information of two biometrics (one digital fingerprint for each user) as security keys of the encryption system. In order to perform the decryption and authentication in a proper way, it is necessary to have the two digital fingerprints from the respective users whose simultaneous authentication is pursued. The proposed security system is developed in the Fourier domain. The nonlinearity of the JTC along with the five security keys given by the three random phase masks and the two digital fingerprints of the two users allow an increase of the system security against brute force and plaintext attacks. The feasibility and validity of this proposal is demonstrated using digital fingerprints as biometrics in numerical experiments.Peer ReviewedPostprint (published version

Effect of wind and atmospheric pressure variations on the mean sea level of salt marshes and estuaries

Se presentan tres formulaciones para predecir las variaciones de largo periodo en el nivel del mar debidas no a la marea astronómica, sino a fenómenos meteorológicos como el viento y los cambios de presión tanto de carácter estacionario como dinámico. Para validar estas fórmulas, se analiza una serie de datos del nivel del mar de tres meses de duración tomada en dos puntos del caño de Sancti Petri separados 5 km entre sí. Se advierten importantes variaciones del nivel medio diario y se demuestra que dichas variaciones son causadas por cambios en la presión atmosférica. Las diferencias son tan importantes (llegan a ser de 26 cm en cuatro días y de 50 cm en un mes y medio) que no pueden ser explicadas únicamente por el factor barométrico invertido (FBI) estático y debemos acudir a la hipótesis dinámica. Los valores ajustados del FBI real oscilan entre 1.9 y 2.2 cm/mb, el doble de lo generalmente utilizado. Se proporciona una acotación superior de la fórmula, de fácil aplicación, para el FBI dinámico. Debido a la morfología y dimensiones del caño, el efecto del viento fue despreciable en este caso. Como conclusión, debe destacarse que cualquier estudio que persiga encontrar la determinación de niveles máximos del mar en estuarios y marismas, con vistas a la delimitación del dominio público marítimo terrestre o de zonas inundables, deberá considerar series de datos de un año mínimo de duración. En caso contrario, la predicción será siempre inferior a los valores reales.The article presents three formulas to predict long-term variations in sea level due not to astronomical tide but to weather effects such as the wind and changes in pressure of both seasonal and dynamic nature. In order to validate these formulas, an analysis was made of a series of sea level data recorded, over a period of three months, at two points in the Sancti Petri Channel spaced 5 km apart. Considerable variations were noted in the daily mean sea level and these variations have been shown to have been caused by changes in the atmospheric pressure. The differences are so large (as much as 26 cm in four days and 50 cm in six weeks) that they cannot be purely explained by the static inverted barometer effect (IBE) and we must then resort to a dynamic hypothesis. The adjusted values of the real IBE vary between 1.9 and 2.2 cm/mb, twice that generally employed. An easily applicable upper limit of the formula for the dynamic IBE is provided. On account of the form and the dimensions of the channel, the wind effect is negligible in this case. By way of conclusion it is indicated that any study attempting to establish the maximum sea levels in estuaries and salt marshes, in order to mark the boundaries of public-owned coastal zones or floodable areas, would require an examination of a series of data covering at least one year. If this is not the case, the forecast will always be lower than the real values

Effects of using an encrypted image corrupted by noise and occlusion in a security system based on joint transform correlator and Gyrator transform

Postprint (published version

Image quality and security through nonlinear joint transform encryption

Postprint (published version

Solitary-wave vortices in quadratic nonlinear media

We find families of vortex solitary waves in bulk quadratic nonlinear media under conditions for second-harmonic generation. We show that the vortex solitary waves are azimuthally unstable and that they decay into sets of stable spatial solitons. We calculate the growth rates of the azimuthal perturbations and show how those affect the pattern of output light. © 1998 Optical Society of AmericaPeer ReviewedPostprint (published version

Hamilton-Jacobi approach to Potential Functions in Information Geometry

The search for a potential function $S$ allowing to reconstruct a given metric tensor $g$ and a given symmetric covariant tensor $T$ on a manifold $\mathcal{M}$ is formulated as the Hamilton-Jacobi problem associated with a canonically defined Lagrangian on $T\mathcal{M}$. The connection between this problem, the geometric structure of the space of pure states of quantum mechanics, and the theory of contrast functions of classical information geometry is outlined.Comment: 16 pages. A discussion on the Kullback-Leibler divergence has been added. To appear in Journal of Mathematical Physic