Low-Complexity LP Decoding of Nonbinary Linear Codes

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. LP decoding has been derived for binary and nonbinary linear codes. However, the most important problem with LP decoding for both binary and nonbinary linear codes is that the complexity of standard LP solvers such as the simplex algorithm remains prohibitively large for codes of moderate to large block length. To address this problem, two low-complexity LP (LCLP) decoding algorithms for binary linear codes have been proposed by Vontobel and Koetter, henceforth called the basic LCLP decoding algorithm and the subgradient LCLP decoding algorithm. In this paper, we generalize these LCLP decoding algorithms to nonbinary linear codes. The computational complexity per iteration of the proposed nonbinary LCLP decoding algorithms scales linearly with the block length of the code. A modified BCJR algorithm for efficient check-node calculations in the nonbinary basic LCLP decoding algorithm is also proposed, which has complexity linear in the check node degree. Several simulation results are presented for nonbinary LDPC codes defined over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and 8-phase-shift keying, respectively, over the AWGN channel. It is shown that for some group-structured LDPC codes, the error-correcting performance of the nonbinary LCLP decoding algorithms is similar to or better than that of the min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201

Stochastic Subgradient Algorithms for Strongly Convex Optimization over Distributed Networks

We study diffusion and consensus based optimization of a sum of unknown convex objective functions over distributed networks. The only access to these functions is through stochastic gradient oracles, each of which is only available at a different node, and a limited number of gradient oracle calls is allowed at each node. In this framework, we introduce a convex optimization algorithm based on the stochastic gradient descent (SGD) updates. Particularly, we use a carefully designed time-dependent weighted averaging of the SGD iterates, which yields a convergence rate of $O\left(\frac{N\sqrt{N}}{T}\right)$ after $T$ gradient updates for each node on a network of $N$ nodes. We then show that after $T$ gradient oracle calls, the average SGD iterate achieves a mean square deviation (MSD) of $O\left(\frac{\sqrt{N}}{T}\right)$. This rate of convergence is optimal as it matches the performance lower bound up to constant terms. Similar to the SGD algorithm, the computational complexity of the proposed algorithm also scales linearly with the dimensionality of the data. Furthermore, the communication load of the proposed method is the same as the communication load of the SGD algorithm. Thus, the proposed algorithm is highly efficient in terms of complexity and communication load. We illustrate the merits of the algorithm with respect to the state-of-art methods over benchmark real life data sets and widely studied network topologies

Electrodynamics of an omega-band as deduced from optical and magnetometer data

We investigate an omega-band event that took place above northern Scandinavia around 02:00–02:30 UT on 9 March 1999. In our analysis we use ground based magnetometer, optical and riometer measurements together with satellite based optical images. The optical and riometer data are used to estimate the ionospheric Hall and Pedersen conductances, while ionospheric equivalent currents are obtained from the magnetometer measurements. These data sets are used as input in a local KRM calculation, which gives the ionospheric potential electric field as output, thus giving us a complete picture of the ionospheric electrodynamic state during the omega-band event. <br><br> The overall structure of the electric field and field-aligned current (FAC) provided by the local KRM method are in good agreement with previous studies. Also the <I><B>E</B></I>&times;<I><B>B</B></I> drift velocity calculated from the local KRM solution is in good qualitative agreement with the plasma velocity measured by the Finnish CUTLASS radar, giving further support for the new local KRM method. The high-resolution conductance estimates allow us to discern the detailed structure of the omega-band current system. The highest Hall and Pedersen conductances, ~50 and ~25 S, respectively, are found at the edges of the bright auroral tongue. Inside the tongue, conductances are somewhat smaller, but still significantly higher than typical background values. The electric field shows a converging pattern around the tongues, and the field strength drops from ~40 mV/m found at optically dark regions to ~10 mV/m inside the areas of enhanced conductivity. Downward FAC flow in the dark regions, while upward currents flow inside the auroral tongue. Additionally, sharp conductance gradients at the edge of an auroral tongue are associated with narrow strips of intense FACs, so that a strip of downward current flows at the eastern (leading) edge and a similar strip of upward current is present at the western (trailing) edge. The Joule heating follows the electric field pattern, so that it is diminished inside the bright auroral tongue

Joint Bayesian endmember extraction and linear unmixing for hyperspectral imagery

This paper studies a fully Bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery. Each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model. The estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical Bayesian model. This model assumes conjugate prior distributions for these parameters, accounts for non-negativity and full-additivity constraints, and exploits the fact that the endmember proportions lie on a lower dimensional simplex. A Gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution. This sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples. The accuracy of the joint Bayesian estimator is illustrated by simulations conducted on synthetic and real AVIRIS images

Economic Integration

The results of international trade have generated a set of both winners and losers. On one side we have the big companies and big producers that stand out and on the other hand, there is a sector that has been affected such as groups of peasants, rural communities, cooperatives, amongst others that live in the poor southern countries. Therefore, the objective of this research article is the search and the design of mechanisms that will counteract the flaws of the current systems, and that will translate into social policies to give a solution to the more unprotected people. Fair trade is an alternative that is heading towards practices of a more social and solidary economy and through these mechanisms, that are funded in

Webb Dock Container Terminal Pavements Ten Years On

SUMMARY Various parts of the Webb Dock Container Terminal have been paved with heavy duty flexible crushed rock pavements, incorporating interlocking concrete segmental pavers for the surfacing. Webb Dock No.5 Terminal, comprising 6 hectares of container stack area, was constructed in 1981, and the Webb Dock Rail Terminal, of a further 2 hectares, was completed in 1985. The performance of the pavements has been entirely satisfactory, despite loads on the pavements substantially exceeding the design loads over the life of the pavements. This paper reviews the design, construction and performance of these pavements up to ten years after being put into service

Social Services Will Not Touch us with a Barge Pole’: Social Care Provision for Older Prisoners

Older prisoners are the fastest growing subgroup in the English and Welsh prison estate. Older prisoners have high levels of health and social care needs. This mixed method study involved the distribution of a questionnaire examining the availability of health and social care services for older prisoners to all prisons housing adult males in England and Wales, followed by qualitative telephone interviews with representatives from eight prisons. Over half of establishments had some contact with external social care services but reported significant difficulties in arranging care for individuals. A professional lead for older prisoners had been identified in 81% of establishments; however the value of this role to positively affect practice appeared questionable. Statutory social care was often non-existent in prison due to the lack of understanding of what it constituted and who was responsible for its provision