Efficient Methods for Finding Optimal Convolutional Self-Doubly Orthogonal Codes

Résumé: Au cours des dernières années, la hausse sans précédent du nombre d'ultrabooks et d'appareils mobiles s'est accompagnée d'un besoin toujours croissant d'accès aux technologies permettant des communications sans-fil fiables et à haut débit. Pour atténuer ou éliminer les erreurs induites par les interférences et le bruit dans les canaux de communication, il est important de développer des systèmes de codage efficaces pour la correction d'erreurs. En effet, lors de communications de données numériques sur un canal ayant un faible rapport signal sur bruit, ces codes permettent de conserver un taux d'erreur faible tout en augmentant le débit des transmissions et/ou en diminuant la puissance d'émission requise. Ceci contribue grandement à améliorer l'efficacité énergétique de ces dispositifs électroniques sans-fil et, ainsi, à prolonger leur autonomie. Dans cette thèse par articles, nous présentons un algorithme de recherche efficace pour trouver deux types de codes correcteurs d'erreur: les codes convolutionnels doublement orthogonaux (CDO) et les codes convolutionnels doublement orthogonaux simplifiés (S-CDO). En effet, ces codes sont utilisés dans un système de contrôle d'erreurs ayant un décodage à seuil itératif différent de la procédure de décodage Turbo classique, puisqu'il ne nécessite aucun entrelaceur, ni à l'encodage, ni aux étapes de décodage. Néanmoins, son processus de décodage à seuil nécessite que ces codes convolutionnels systématiques satisfassent des propriétés dites de « double orthogonalité », allant au-delà des conditions requises par les codes « simplement orthogonaux », bien connus et habituellement utilisés lors d'un décodage à seuil non-itératif. Afin de pouvoir construire des codecs à haute performance et à faible latence avec ces codes, il est important de minimiser leur longueur de contrainte ou « span » pour un nombre J de connexions donné. Bien que trouver des codes CDO et S-CDO ne soit pas difficile, déterminer les codes ayant un span minimal (dit optimal) pour un ordre J donné est mathématiquement très complexe. En effet, la construction directe de codes CDO / S-CDO à span court/optimal reste un problème ouvert et qui est soupçonné d'être NP-complet. Cette thèse présente un total de trois articles: deux articles publiés dans IEEE Transactions on Communications et un article soumis au journal IEEE Transactions on Parallel and Distributed Systems . Dans ces articles, nous décrivons un nouvel algorithme de recherche parallèle, efficace et implicitement-exhaustif pour trouver des codes CDO et S-CDO systématiques, à taux R=1/2 et ayant un span plus court, voire minimal, c.à.d. optimal. Comparé à l'algorithme de recherche implicitement-exhaustif de référence, l'algorithme de recherche à haute performance proposé reste exhaustif mais fournit un facteur d'accélération très important, supérieur à 16300 pour les codes CDO (J=7) et supérieur à 6300 pour les codes S-CDO (J=8).----------Abstract: In recent years, the rise of ultrabooks and mobile devices has been accompanied by an ever increasing need for reliable high-bandwidth wireless communications. To mitigate or eliminate the errors that are invariably introduced due to noise and interference in the communication channels, it is important to develop efficient error-correcting coding schemes. Indeed, these codes may be used to preserve the error performance while allowing the data-rate of digital communications to be increased and the transmission power at lower signal-to-noise ratios to be reduced, thereby improving the overall power efficiency of these devices. In this manuscript-based thesis, we present an efficient search algorithm for finding optimal/short-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified Convolutional Self-Doubly Orthogonal (S-CDO) codes. These error-correcting codes are employed in an iterative error-control coding scheme that differs from the classical Turbo code procedure, as it does not require any interleaver, neither at the encoding nor at the decoding stages. However, its iterative threshold decoding procedure requires that these systematic convolutional codes satisfy some “double orthogonality properties”, beyond those of the well-known orthogonal codes used in the usual non-iterative threshold decoding. In order to build high-performance, low-latency codecs with these codes, it is important to minimize the constraint length, also called “span”, for a given number J of generator connections. Although finding CDO/S-CDO codes is not difficult, determining the optimal/short-span codes for a given order J is computationally very challenging. The direct construction of optimal or shortest-span CDO and S-CDO codes has so far eluded analysis, and the search for these codes is believed to be an NP-complete problem. The thesis presents a total of three articles: two articles that were published in IEEE Transactions on Communications , and one article that was submitted for publication to IEEE Transactions on Parallel and Distributed Systems . In these articles, we describe a novel efficient and parallel implicitly-exhaustive search algorithm for finding rate R=1/2 systematic optimal/short-span CDO and S-CDO codes. The high-performance search algorithm is still exhaustive in nature, yet it provides an impressive speedup that is larger than 16300 (CDO, J=7) and 6300 (S-CDO, J=8) over the reference implicitly-exhaustive search algorithm, and larger than 2000 (CDO, J=17) over the fastest known CDO validation function used in high-performance pseudo-random search algorithms

Combinatorial Optimization

Combinatorial Optimization is a very active field that benefits from bringing together ideas from different areas, e.g., graph theory and combinatorics, matroids and submodularity, connectivity and network flows, approximation algorithms and mathematical programming, discrete and computational geometry, discrete and continuous problems, algebraic and geometric methods, and applications. We continued the long tradition of triannual Oberwolfach workshops, bringing together the best researchers from the above areas, discovering new connections, and establishing new and deepening existing international collaborations

Deep learning applied to the assessment of online student programming exercises

Massive online open courses (MOOCs) teaching coding are increasing in number and popularity. They commonly include homework assignments in which the students must write code that is evaluated by functional tests. Functional testing may to some extent be automated however provision of more qualitative evaluation and feedback may be prohibitively labor-intensive. Provision of qualitative evaluation at scale, automatically, is the subject of much research effort. In this thesis, deep learning is applied to the task of performing automatic assessment of source code, with a focus on provision of qualitative feedback. Four tasks: language modeling, detecting idiomatic code, semantic code search, and predicting variable names are considered in detail. First, deep learning models are applied to the task of language modeling source code. A comparison is made between the performance of different deep learning language models, and it is shown how language models can be used for source code auto-completion. It is also demonstrated how language models trained on source code can be used for transfer learning, providing improved performance on other tasks. Next, an analysis is made on how the language models from the previous task can be used to detect idiomatic code. It is shown that these language models are able to locate where a student has deviated from correct code idioms. These locations can be highlighted to the student in order to provide qualitative feedback. Then, results are shown on semantic code search, again comparing the performance across a variety of deep learning models. It is demonstrated how semantic code search can be used to reduce the time taken for qualitative evaluation, by automatically pairing a student submission with an instructor’s hand-written feedback. Finally, it is examined how deep learning can be used to predict variable names within source code. These models can be used in a qualitative evaluation setting where the deep learning models can be used to suggest more appropriate variable names. It is also shown that these models can even be used to predict the presence of functional errors. Novel experimental results show that: fine-tuning a pre-trained language model is an effective way to improve performance across a variety of tasks on source code, improving performance by 5% on average; pre-trained language models can be used as zero-shot learners across a variety of tasks, with the zero-shot performance of some architectures outperforming the fine-tuned performance of others; and that language models can be used to detect both semantic and syntactic errors. Other novel findings include: removing the non-variable tokens within source code has negligible impact on the performance of models, and that these remaining tokens can be shuffled with only a minimal decrease in performance.Engineering and Physical Sciences Research Council (EPSRC) fundin

Proceedings of the 3rd Annual Conference on Aerospace Computational Control, volume 1

Conference topics included definition of tool requirements, advanced multibody component representation descriptions, model reduction, parallel computation, real time simulation, control design and analysis software, user interface issues, testing and verification, and applications to spacecraft, robotics, and aircraft

Solving Multi-objective Integer Programs using Convex Preference Cones

Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron víctimas de algún tipo de delito y la manera en que ocurrió el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en Méxic

Proceedings of the 2nd Conference on Production Systems and Logistics (CPSL 2021)

Proceedings of the CPSL 202

1991 OURE report, including the 1st Annual UMR Undergraduate Research Symposium -- Entire Proceedings

The Opportunities for Undergraduate Research Experiences program began in 1990. The aims were to enrich the learning process and make it more active, encourage interaction between students and faculty members, raise the level of research on the campus, help recruit superior students to the graduate program, and support the notion that teaching and research are compatible and mutually reinforcing. Chancellor Jischke made available an annual budget of $50,000 to support the program. As the papers herein attest, the OURE program is achieving its goals — UMR graduates have performed research on an enormous variety of topics, have worked closely with faculty members, and have experienced deeply both the pleasures and frustrations of research. Several of the undergraduates whose papers are included are now graduate students at UMR or elsewhere. Others, who have not yet graduated, are eager to submit proposals to the next OURE round. I am sure all involved join me in expressing gratitude to Chancellor Jischke for inaugurating the program. The first section of this volume is made up of papers presented at the first annual UMR Undergraduate Research Symposium, held in April 1991. Joining the UMR undergraduates in the Symposium were students from other colleges and universities who had participated in an NSF- sponsored summer program of research on parallel processing conducted by the UMR Computer Science Department