The Euclidean Algorithm for Generalized Minimum Distance Decoding of Reed-Solomon Codes

This paper presents a method to merge Generalized Minimum Distance decoding of Reed-Solomon codes with the extended Euclidean algorithm. By merge, we mean that the steps taken to perform the Generalized Minimum Distance decoding are similar to those performed by the extended Euclidean algorithm. The resulting algorithm has a complexity of O(n^2)

On the Equivalence of Sudan-Decoding and Decoding via Virtual Extension to an Interleaved Reed-Solomon Code

International audienceIn this paper we investigate two new decoding schemes for Reed-Solomon codes, which allow to decode beyond half the minimum distance. One is Sudan's list-decoding principle, based on interpolation with a degree-restricted bivariate polynomial. We show a syndrome-based approach of it. We compare Sudan's procedure with a scheme that is based on an extension to Interleaved Reed-Solomon codes. We present theoretical parallels and outline both algorithms in a unique comparable way. Furthermore, we show the connection of both schemes to the classical Linear Feedback Shift Register analysis. Afterwards, we compare the performance of the considered schemes

Video and course content discussion on Massive Open Online Courses: An exploratory research

This paper deals with the ways in which Massive Open Online Courses (MOOC) participants use course related forums and the contribution of those forums to the learning experience of their virtual students. We focused on the comparison between, on one hand, video content provided by the course organizers and on the other hand, the content provided by user discussions in the forums. Our methodology frame is based on natural sociological inquiry. Video Lectures, as well as the most active forum threads and their posts were collected during a 6 weeks long xMOOC that took place in fall 2013 on a well-known MOOC platform. Content analysis was performed and the study concludes that the forum included a very high level of interactions involving mostly course related exchange of information amongst students, placing this course at the intersection between a constructivist MOOC (cMOOC) and a classical information transmission based MOOC (xMOOC)

Decoding Hermitian codes - an engineering approach

This thesis introduces and discusses a new algorithm for solving the key equation for Hermitian codes, that belong to the class of algebraic-geometric (AG) codes. First, the most important concepts of channel coding are recalled and the popular Reed-Solomon (RS) codes are used to illustrate them. The decoding of RS codes with the extended Euclidean algorithm is used to illustrate the basic idea of algebraic decoding and motivate the new decoding algorithm. After that, some elementary results from algebraic geometry, that are (directly or indirectly) used in the definition of AG codes, are introduced. From the definition of general AG codes, RS codes and Hermitian codes are derived as special cases. An alternative definition of Hermitian codes that uses almost no algebraic geometry is also given. After that, the key equation for Hermitian codes is presented. For a limited error weight, it has a unique solution of minimal degree, and the error pattern can be reconstructed from this solution. An algorithm that finds this solution of minimal degree is given. But this algorithm is not capable of decoding all error patterns with weight up to half the minimum distance - a bound up to which unique decoding is guaranteed by the properties of general linear codes. An extension that achieves this decoding radius is discussed afterwards, and the complexity of both the algorithm and its extension are estimated. A modification of the algorithm that returns a basis for decoding beyond half the minimum distance is given in the last chapter. However, decoding up to this increased radius without (significantly) increasing the complexity is not always possible. A bound on the error weight that allows such decoding for interleaved Hermitian codes with high probability is derived, as well as the probability that decoding fails. Finally, the idea of virtual extension to an interleaved code is described. This principle works only for codes with low rates, and the rate bound is given

On the Equivalence of Sudan-Decoding and Decoding via Virtual Extension to an Interleaved Reed-Solomon Code

Abstract-In this paper we investigate two new decoding schemes for Reed-Solomon codes, which allow to decode beyond half the minimum distance. One is Sudan's list-decoding principle, based on interpolation with a degree-restricted bivariate polynomial. We show a syndrome-based approach of it. We compare Sudan's procedure with a scheme that is based on an extension to Interleaved Reed-Solomon codes. We present theoretical parallels and outline both algorithms in a unique comparable way. Furthermore, we show the connection of both schemes to the classical Linear Feedback Shift Register analysis. Afterwards, we compare the performance of the considered schemes. Index Terms-Interleaved Reed-Solomon (IRS) codes, Suda

“What and how do we learn from LinkedIn forums?” an exploratory investigation

This study examines several academic and professional LinkedIn forums, and using a grounded theory perspective, observes three key lifelong learning interactions for participants—a) problem solving through shared learning and helping processes,” b) a technical features learning center for learning new interfaces and features, and c) social networking. These three interactions offer a preliminary understanding of the potential for LinkedIn forums as a lifelong learning space, and an innovation space where weak ties and transactive memory systems have the potential to affect multidisciplinary and transdisciplinary research practices, as well as create economic value for higher education by connecting active researchers to industry and other researchers

Experiencing global culture in Vatel ::implications of using knowledge management concepts for approaching culture in professional communication

To explore the meaning of “global culture” in a professional communication context, this paper explores the “unsettled” global culture of Vatel, a private business school educating students from nearly 50 different countries for the hospitality industry. This paper explores the role of knowledge management in understanding global culture, arguing that the notion of “unsettled” cultures demonstrates how ideologies function in global settings and draw on national “settled” cultural resources. In unpacking different aspects of Vatel's culture this paper questions assumptions built into cultural frames of reference by offering a global culture frame, drawing on cultural resources from country based “settled” cultural contexts, and reflects on how global cultural contexts can benefit from a knowledge management approach to this dynamic between “settled” cultural contexts and “unsettled” cultural ideologies that frame global cultural experiences. This approach to culture offers an opportunity for professional and technical communicators to reflect on global cultural contexts in the workplace

Analogues of cis- and transplatin with a rich solutionchemistry: Cis-[PtCl2(NH3)(1-MeC-N3)] and trans-[PtI2(NH3)(1-MeC-N3)]

Mono(nucleobase) complexes of the general composition cis-[PtCl(NH)L] with L=1-methylcytosine, 1-MeC (1 a) and L=1-ethyl-5-methylcytosine, as well as trans-[PtX(NH)(1-MeC)] with X=I (5 a) and X=Br (5 b) have been isolated and were characterized by X-ray crystallography. The Pt coordination occurs through the N3 atom of the cytosine in all cases. The diaqua complexes of compounds 1 a and 5 a, cis-[Pt(HO)(NH)(1-MeC)] and trans-[Pt(HO)(NH)(1-MeC)], display a rich chemistry in aqueous solution, which is dominated by extensive condensation reactions leading to μ-OH- and μ-(1-MeC-N3,N4)-bridged species and ready oxidation of Pt to mixed-valence state complexes as well as diplatinum(III) compounds, one of which was characterized by X-ray crystallography: h,t-[{Pt(NH)(OH)(1-MeC-N3,N4)}](NO).2 [NH](NO).2 HO. A combination of H NMR spectroscopy and ESI mass spectrometry was applied to identify some of the various species present in solution and the gas phase, respectively. As it turned out, mass spectrometry did not permit an unambiguous assignment of the structures of +1 cations due to the possibilities of realizing multiple bridging patterns in isomeric species, the occurrence of different tautomers, and uncertainties regarding the Pt oxidation states. Additionally, compound 1 a was found to have selective and moderate antiproliferative activity for a human cervix cancer line (SISO) compared to six other human cancer cell lines.This work was supported by the Deutsche Forschungsgemeinschaft. P.J.S.M. thanks the Spanish Ministry of Economy and Competitiveness for funding through the Ramón y Cajal program.Peer Reviewe

Generalized moment analysis of magnetic field correlations for accumulations of spherical and cylindrical magnetic perturbers

In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin dephasing in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows deriving analytical expressions of the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times