H2020Индивидуална стипендия2018–2020

ACCENT · Algebraic Covering Codes Enabling Network Transmissions

„Хоризонт 2020“ — Действия „Мария Склодовска-Кюри“

Период: 2018-05-01 → 2020-04-30
Финансиране от ЕС: 175 866 €
Участници: 1
Схема: MSCA-IF

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Накратко на български

Математическите свойства на кодовете за коригиране на грешки с рангова метрика анализират как се разпределят данните при предаване в мрежи. Това помага за ограничаване на усилването на грешките в комуникациите между компютри и устройства.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Algebraic Covering Codes Enabling Network Transmissions

The research focus of the project was on the mathematical properties of rank-metric error-correcting codes, with emphasis of their covering radii, (generalized) weight distributions, density properties and structural invariants. More details are included in the section “Progress beyond the state of the art”. Rank-metric codes were proposed in 2008 as a solution to the problem of error amplification in network communications. Since then, they have been the subject of intense research among mathematicians, electrical engineers and computer scientists. Besides the research objectives, the project also had the goal of strengthen the professional profile of the researcher and enhance his career perspectives via mentoring experience, training in proposal writing, and teaching experience.

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

Applications of rank-metric codes arise ever more frequently in network communications problems, and yet their mathematical theory is still in its infancy. To date attention has almost exclusively focussed on very special classes of codes and their generalizations. The covering problem for rank-metric codes is largely unsolved, and is an important combinatorial research topic. For error-free paradigms, codes with low covering radius provide efficient solutions for broadcast problems, and specifically to optimizing content delivery networks for large files distribution. Current approaches to such applications are suboptimal, while known methods to obtaining best possible performance are computationally infeasible. For error-correcting schemes, the covering radius is an important indicator of code performance, as it measures the number of errors that can be corrected in network transmissions.We propose to develop a mathematical theory of covering codes for the rank metric. We will obtain bounds on the covering radius of an arbitrary rank-metric code, as well as special classes of codes. We will develop the fundamental tools required to pioneer this theory, offering scope for researchers of Algebraic Coding Theory, as well as combinatorial objects useful for Engineering applications. We will also investigate symmetric rank-metric codes, focussing on their distance distributions. These codes have a very rich combinatorial structure.The combined expertise of the Applied Algebra group at UCD, along with the methods developed by the applicant in his PhD, will propel the project to achieve its objectives. The potential scientific impact is high, given the newness and combinatorial hardness of the topic, its importance for network communications, and exponentially increasing data traffic. The impact for the applicant will be the opportunity to establish this fundamental topic, magnify his scientific profile, and consolidate/expand his professional network.

Оригинален текст от CORDIS (на английски).

Участници

UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN · DublinКоординаторИрландия