An improvement to multifold euclidean geometry codes

This paper presents an improvement to the multifold Euclidean geometry codes introduced by Lin (1973).The improved multifold EG codes are proved to be maximal, and therefore they are more efficient than the multifold EG codes. Relationships between the improved multifold EG codes and other known majority-logic decodable codes are proved

Zakopane lectures on loop gravity

These are introductory lectures on loop quantum gravity. The theory is presented in self-contained form, without emphasis on its derivation from classical general relativity. Dynamics is given in the covariant form. Some applications are described.Comment: This is a largely restructured and expanded version of the lectures. In particular, I have added a substantial introductory and orientation Section, a discussion on the justification for the vertex expansion, and more details on the applications. Comments and corrections always very welcome. 34 pages. Many figure

Some new results on majority-logic codes for correction of random errors

The main advantages of random error-correcting majority-logic codes and majority-logic decoding in general are well known and two-fold. Firstly, they offer a partial solution to a classical coding theory problem, that of decoder complexity. Secondly, a majority-logic decoder inherently corrects many more random error patterns than the minimum distance of the code implies is possible. The solution to the decoder complexity is only a partial one because there are circumstances under which a majority-logic decoder is too complex and expensive to implement. [Continues.

Research in the Aloha system

The Aloha system was studied and developed and extended to advanced forms of computer communications networks. Theoretical and simulation studies of Aloha type radio channels for use in packet switched communications networks were performed. Improved versions of the Aloha communications techniques and their extensions were tested experimentally. A packet radio repeater suitable for use with the Aloha system operational network was developed. General studies of the organization of multiprocessor systems centered on the development of the BCC 500 computer were concluded

Majority-Logic-Decodierung für Euklidische-Geometrie-Codes

Diese Arbeit befasst sich mit Majority-Logic-Decodieralgorithmen für Euklidische-Geometrie-Codes. Diese Verfahren zeichnen sich dadurch aus, auf Hardwareebene in Echtzeit unter Verteilung des Rechenaufwands auf mehrere Prozessoren decodieren zu können. Das Ziel der vorliegenden Dissertation ist es, die bestehenden Majority-Logic-Decodierverfahren, insbesondere den Reed-Algorithmus, hinsichtlich der Performanz zu verbessern beziehungsweise neue, effizientere Verfahren zu entwickeln. Wir werden zwei neue Algorithmen vor- stellen, bei denen die Anzahl der auszuführenden Mehrheitsentscheidungen signifikant reduziert ist. Einer der beiden Algorithmen basiert wie jener von Reed einzig auf Mehrheitsentscheidungen. Der andere Algorithmus verwendet zusätzlich Additionen bzw. Subtraktionen, so dass weniger Mehrheitsentscheidungen als bei den anderen beiden Algorithmen getroffen werden müssen. Darüber hinaus haben wir eine neue Abstufung konstruiert, mit der wir unabhängig vom verwendeten Decodierverfahren mindestens die gleichen oder bessere Ergebnisse als Chen und Reed erzielen, so dass diese aus Gründen der Performanz stets vorzuziehen ist. Die vorliegende Dissertation enthält zudem eine genaue Analyse des Aufwands der Majority-Logic-Decodierverfahren, einschließlich des Reed-Algorithmus, angewandt auf verschiedene Codeklassen wie Hamming-Codes, Reed-Muller-Codes, Euklidische-Geometrie-Codes sowie zweifache Euklidische-Geometrie- Codes. Darauf basierend sprechen wir Empfehlungen aus, welche Codes mit welcher Parameterwahl (bei gleichen Fehlerkorrektureigenschaften) die höchste Performanz bieten

Rigorous direct and inverse design of photonic-plasmonic nanostructures

Designing photonic-plasmonic nanostructures with desirable electromagnetic properties is a central problem in modern photonics engineering. As limited by available materials, engineering geometry of optical materials at both element and array levels becomes the key to solve this problem. In this thesis, I present my work on the development of novel methods and design strategies for photonic-plasmonic structures and metamaterials, including novel Green’s matrix-based spectral methods for predicting the optical properties of large-scale nanostructures of arbitrary geometry. From engineering elements to arrays, I begin my thesis addressing toroidal electrodynamics as an emerging approach to enhance light absorption in designed nanodisks by geometrically creating anapole configurations using high-index dielectric materials. This work demonstrates enhanced absorption rates driven by multipolar decomposition of current distributions involving toroidal multipole moments for the first time. I also present my work on designing helical nano-antennas using the rigorous Surface Integral Equations method. The helical nano-antennas feature unprecedented beam-forming and polarization tunability controlled by their geometrical parameters, and can be understood from the array perspective. In these projects, optimization of optical performances are translated into systematic study of identifiable geometric parameters. However, while array-geometry engineering presents multiple advantages, including physical intuition, versatility in design, and ease of fabrication, there is currently no rigorous and efficient solution for designing complex resonances in large-scale systems from an available set of geometrical parameters. In order to achieve this important goal, I developed an efficient numerical code based on the Green’s matrix method for modeling scattering by arbitrary arrays of coupled electric and magnetic dipoles, and show its relevance to the design of light localization and scattering resonances in deterministic aperiodic geometries. I will show how universal properties driven by the aperiodic geometries of the scattering arrays can be obtained by studying the spectral statistics of the corresponding Green’s matrices and how this approach leads to novel metamaterials for the visible and near-infrared spectral ranges. Within the thesis, I also present my collaborative works as examples of direct and inverse designs of nanostructures for photonics applications, including plasmonic sensing, optical antennas, and radiation shaping