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

Cryptanalysis of ARX-based White-box Implementations

At CRYPTO’22, Ranea, Vandersmissen, and Preneel proposed a new way to design white-box implementations of ARX-based ciphers using so-called implicit functions and quadratic-affine encodings. They suggest the Speck block-cipher as an example target. In this work, we describe practical attacks on the construction. For the implementation without one of the external encodings, we describe a simple algebraic key recovery attack. If both external encodings are used (the main scenario suggested by the authors), we propose optimization and inversion attacks, followed by our main result - a multiple-step round decomposition attack and a decomposition-based key recovery attack. Our attacks only use the white-box round functions as oracles and do not rely on their description. We implemented and verified experimentally attacks on white-box instances of Speck-32/64 and Speck-64/128. We conclude that a single ARX-round is too weak to be used as a white-box round

The alignments and clustering of galaxies in wide-area photometric galaxy surveys

The upcoming decades will see the transformation of our understanding of the Universe. New experiments, soon to come online, aim to observe the evolution of large-scale structures traced by billions of galaxies, throughout much of cosmic time. The volume of data soon to be at our disposal comes with responsibility; with unprecedented levels of statistical power, we must identify and control sources of systematic error in our analyses to an ever greater degree, lest we waste newfound precision upon inaccurate inferences. This thesis explores the impacts of such errors upon our understanding of galaxy data, and proposes methods for their mitigation. First, I detail my study of the intrinsic alignments of galaxies (Ch. 2). The study of weak cosmological lensing (or `cosmic shear') posits that the distribution of intrinsic galaxy shapes should be random, and thus that we can learn about the Universe by attributing shape correlations to the effects of gravitational lensing by the large-scale structure. However, we observe different galaxies to be intrinsically aligned with structure in complex ways; violating the assumption of randomness and forming the primary astrophysical systematic for cosmic shear analyses. Using a unique set of highly-complete, spectroscopic data, I directly measure and model the projected 3D galaxy intrinsic alignments and clustering, revealing new complexity regarding the spiral/elliptical, central/satellite nature of galaxies, before forecasting the benefits of my data-driven priors for intrinsic alignment models in future cosmic shear work. The physical galaxy distribution is another powerful probe of the Universe, however, measurements of galaxy clustering must contend with spatially non-uniform observing conditions. If poor conditions result in systematic failures to detect objects, the observed clustering will not represent the true galaxy density field. I describe (in Ch. 3) a method of mitigation for such biases, centred around the retrieval of systematic density modes from galaxy data using self-organising maps (SOMs). Creating random galaxy catalogues which mimic and thereby subtract the systematic density trends, I demonstrate the accurate recovery of clustering signals from realistically deprecated synthetic data. I go on to present the first photometric angular clustering measurement from the Kilo Degree Survey, made robust by our corrective randoms. Studies of 3D, or projected, clustering and intrinsic alignments are typically limited to spectroscopic, rather than photometric, data; accurate redshifts are necessary to isolate objects in the radial dimension. The Physics of the Accelerating Universe Survey bridges this gap, offering greater depths at a small cost to redshift accuracy, by observing in 40 optical narrow-bands. In Ch. 4, I derive principled random galaxy catalogues, capable of reproducing the galaxies' redshift distribution sans structure, and doing so robustly for arbitrary galaxy sample selections. With these randoms, I explore the projected 3D clustering and intrinsic alignments of these data, finding quite remarkable support for the conclusions of my previous work (Ch 2), and extending the study of intrinsic alignments to yet fainter objects and smaller scales

Cosmological information from moments and Bayesian reconstruction methods

This thesis explores novel ways on constraining the cosmological model of our Universe with observational data. The explosion in high fidelity data coupled with the increasing number of complementary cosmological probes, makes it possible to test our theories to an unprecedented precision. However, reaching the experimental designed precision for the upcoming surveys will require advances in theoretical and statistical modelling. We contribute work to two avenues addressing this problem, in particular by extracting nongaussian information from higher order weak gravitational lensing statistics and by using Bayesian forward modelling approaches to increase the information gain compared to traditional analysis methods. For the first project we focus on the aperture mass statistics, which is a E/B decomposed measure of the weak lensing convergence polyspectra. We construct an accelerated estimator that will make it feasible to measure those statistics in current and forthcoming surveys. After identifying an optimized weighting scheme and adapting the theoretical expressions to account for potential biases, we successfully test the estimators’ performance and reliability on simulated surveys and then measure the second order statistics on the CFHTLenS survey, finding excellent agreement with the traditional analysis in terms of the shear correlation functions. For the second project we move away from summary statistics and shift our focus to the cosmic field itself. Using idealized structure formation models we construct a likelihood function for a linearized cosmic field, taking into account the observed realization of tracers. For an effcient sampling of this high dimensional problem we employ a Hamiltonian Monte Carlo framework. We then extend the likelihood to jointly sample the field and the amplitude of its underlying power spectrum. We find that for realistic scale cuts and galaxy number densities this framework increases the information content by a factor of four

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”