In state-of-the-art fiber-optics communication systems the fixed forward error correction (FEC) and constellation size are employed. While it is important to closely approach the Shannon limit by using turbo product codes (TPC) and low-density parity-check (LDPC) codes with soft-decision decoding (SDD) algorithm; rate-adaptive techniques, which enable increased information rates over short links and reliable transmission over long links, are likely to become more important with ever-increasing network traffic demands. In this invited paper, we describe a rate adaptive non-binary LDPC coding technique, and demonstrate its flexibility and good performance exhibiting no error floor at BER down to 10(-15) in entire code rate range, by FPGA-based emulation, making it a viable solution in the next-generation high-speed intelligent aggregation networks.

Forward error correction (FEC) is as one of the key technologies enabling the next-generation high-speed fiber optical communications. In this paper, we propose a rate-adaptive scheme using a class of generalized low-density parity-check (GLDPC) codes with a Hamming code as local code. We show that with the proposed unified GLDPC decoder architecture, a variable net coding gains (NCGs) can be achieved with no error floor at BER down to 10(-15), making it a viable solution in the next-generation high-speed fiber optical communications.

Οι MLC NAND Flash μνήμες παίζουν πρωταγωνιστικό ρόλο για την αποθήκευση δε- δομένων, καθώς έχουν μεγάλη αποθηκευτική ικανότητα λόγω της μεγάλης πυκνότητάς τους, χαμηλό κόστος και χαμηλή απαίτηση σε ισχύ. Για τους λόγους αυτούς, έγινε εφικτό από τους σκληρούς δίσκους οδήγησης (HDDs) πλέον έχουμε περάσει στην εποχή των Solid State Drives (SSDs) που αποτελούν ένα μεγάλο βήμα για την αποθήκευση δεδομένων αποδοτικά και αξιόπιστα. Βέβαια η παρουσία λαθών στις MLC NAND Flash μνήμες, λόγω φαινομένων όπως η γήρανση του υλικού καθιστά απαραίτητη την εφαρμογή κωδίκων διόρθωσης λαθών (ECC) ώστε να διατηρηθεί η αξιοπιστία σε επιθυμητά επίπεδα. Σκοπός λοιπόν αυτής της διπλωματικής είναι αρχικά η ανάπτυξη ενός παραμετροποιήσιμου μοντέλου MLC NAND Flash μνήμης για την εξομοίωση εμφάνισης λαθών. Στη συνέχεια η χρησιμοποίηση soft-decision Low Density Parity Check (LDPC) κωδίκων για τη διόρθωση λαθών με τέτοι οτρόπο ώστε να παρατείνουμε το χρόνο ζωής της μνήμης και τελικά να υπολογίσουμε το Life Time Capacity που αποτελεί το συνολικό μέγεθος της πληροφορίας που μπορεί να αποθηκευθεί σε μία μνήμη καθ’όλη τη διάρκεια ζωής της. / --

Σε διαγράμματα BER, με τα οποία αξιολογείται ένα σύστημα αποκωδικοποίησης, και σε χαμηλά επίπεδα θορύβου, παρατηρείται πολλές φορές η περιοχή Error Floor, όπου η απόδοση του αποκωδικοποιητή δε βελτιώνεται πλέον, καθώς μειώνεται ο θόρυβος. Με πραγματοποίηση εξομοίωσης σε software, το Error Floor συνήθως δεν είναι ορατό, κι έτσι κύριο ζητούμενο είναι η πρόβλεψη της συμπεριφοράς του αποκωδικοποιητή, αλλά και γενικότερα η βελτιστοποίηση της απόδοσής του σε αυτήν την περιοχή. Στην παρούσα διπλωματική εργασία μελετάται η ανεπιτυχής αποκωδικοποίηση ορισμένων κωδικών λέξεων καθώς και ο μηχανισμός ενεργοποίησης των Trapping Sets, δηλαδή δομών, οι οποίες φαίνεται να είναι το κύριο αίτιο εμφάνισης του Error Floor. Xρησιμοποιείται το AWGN μοντέλο καναλιού και κώδικας με αραιό πίνακα ελέγχου ισοτιμίας (LDPC), ενώ οι εξομοιώσεις επαναληπτικών αποκωδικοποιήσεων πραγματοποιούνται σε επίπεδα (Layers), με αλγορίθμους ανταλλαγής μηνυμάτων (Message Passing). Αναλύονται προτεινόμενοι τροποποιημένοι αλγόριθμοι και μελετώνται οι επιπτώσεις του κβαντισμού των δεδομένων. Τέλος, προσδιορίζεται η επίδραση του θορύβου στην αποκωδικοποίηση και αναπτύσσεται ένα ημιαναλυτικό μοντέλο υπολογισμού της πιθανότητας ενεργοποίησης ενός Trapping Set και της πιθανότητας εμφάνισης σφάλματος κατά τη μετάδοση. / In BER plots, which are used in order to evaluate a decoding system, and at low-noise level, the Error Floor region is sometimes observed, where the decoder performance is no longer improved, as noise is reduced. When a simulation is executed using software, the Error Floor region is usually not visible, so the main goal is the prediction of the decoder's behavior, as well as the improvement in general of its performance in that particular region. In this thesis, we study the conditions which result in a decoding failure for specific codewords and a Trapping Set activation. Trapping Sets are structures in a code, which seem to be the main cause of the Error Floor presence in BER plots. For the purpose of our study, we use the AWGN channel model and a linear block code with low density parity check matrix (LDPC), while iterative decoding simulations are executed by splitting the parity check matrix into layers (Layered Decoding) and by using Message Passing algorithms. We propose and analyze three new modified algorithms and we study the effects caused by data quantization. Finally, we determine the noise effects on the decoding procedure and we develop a semi-analytical model used for calculating the probability of a Trapping Set activation and for calculating the error probability during transmission.

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The unifying theme of this dissertation is the development of new solutions for decoding and inference problems based on convex optimization methods. Th first part considers the joint detection and decoding problem for low-density parity-check (LDPC) codes on finite-state channels (FSCs). Hard-disk drives (or magnetic recording systems), where the required error rate (after decoding) is too low to be verifiable by simulation, are most important applications of this research. Recently, LDPC codes have attracted a lot of attention in the magnetic storage industry and some hard-disk drives have started using iterative decoding. Despite progress in the area of reduced-complexity detection and decoding algorithms, there has been some resistance to the deployment of turbo-equalization (TE) structures (with iterative detectors/decoders) in magnetic-recording systems because of error floors and the difficulty of accurately predicting performance at very low error rates. To address this problem for channels with memory, such as FSCs, we propose a new decoding algorithms based on a well-defined convex optimization problem. In particular, it is based on the linear-programing (LP) formulation of the joint decoding problem for LDPC codes over FSCs. It exhibits two favorable properties: provable convergence and predictable error-floors (via pseudo-codeword analysis). Since general-purpose LP solvers are too complex to make the joint LP decoder feasible for practical purposes, we develop an efficient iterative solver for the joint LP decoder by taking advantage of its dual-domain structure. The main advantage of this approach is that it combines the predictability and superior performance of joint LP decoding with the computational complexity of TE. The second part of this dissertation considers the matrix completion problem for the recovery of a data matrix from incomplete, or even corrupted entries of an unknown matrix. Recommender systems are good representatives of this problem, and this research is important for the design of information retrieval systems which require very high scalability. We show that our IMP algorithm reduces the well-known cold-start problem associated with collaborative filtering systems in practice.

At a time where almost 1.75 billion people around the world use the Internet on a regular basis, optical communication over optical fibers that is used in long distance and high demand applications has to be capable of providing higher communication speed and re-liability. In recent years, strong demand is driving the dense wavelength division multip-lexing network upgrade from 10 Gb/s per channel to more spectrally-efficient 40 Gb/s or 100 Gb/s per wavelength channel, and beyond. The 100 Gb/s Ethernet is currently under standardization, and in a couple of years 1 Tb/s Ethernet is going to be standardized as well for different applications, such as the local area networks (LANs) and the wide area networks (WANs). The major concern about such high data rates is the degradation in the signal quality due to linear and non-linear impairments, in particular polarization mode dispersion (PMD) and intrachannel nonlinearities. Moreover, the higher speed transceivers are expensive, so the alternative approaches of achieving the required rates is preferably done using commercially available components operating at lower speeds.In this dissertation, different LDPC-coded modulation techniques are presented to offer a higher spectral efficiency and/or power efficiency, in addition to offering aggregate rates that can go up to 1Tb/s per wavelength. These modulation formats are based on the bit-interleaved coded modulation (BICM) and include: (i) three-dimensional LDPC-coded modulation using hybrid direct and coherent detection, (ii) multidimensional LDPC-coded modulation, (iii) subcarrier-multiplexed four-dimensional LDPC-coded modulation, (iv) hybrid subcarrier/amplitude/phase/polarization LDPC-coded modulation, and (v) iterative polar quantization based LDPC-coded modulation.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: Low earth orbit (LEO) satellite communication presents a unique environment which inherently di ers from most other communication channels. Due to the varying orbital patterns of LEO satellites the link exhibits varying link margins. Limited communication time windows need to be optimised to maximise the volumetric data throughput. Large coding gains can be obtained by the implementation of forward error correction codes. This thesis presents a means for optimising the data throughput of LEO satellite communication through the implementation of a mission speci c error control strategy. Low density parity check (LDPC) codes are versatile and present good error performances at many di erent code rates and block lengths. With power limitations on the space segment and remote ground stations, hardware utilisation e ciency must be optimised to reduce power consumption. In response to this requirement, this thesis evaluates various algorithms for LDPC decoders. An iterative LDPC decoder, implementing an approximation algorithm, is presented as a low complexity solution with good error performance. The proposed solution provides a very good balance between required hardware complexity and coding performance. It was found that many parameters of the decoders and codes can be altered to allow the implementation of these codes in systems with varying memory and processing capabilities. / AFRIKAANSE OPSOMMING: Kommunikasiekanale van satelliete met lae wentelbane, bied 'n unieke omgewing wat inherent verskil van meeste ander kommunikasiekanale. As gevolg van veranderende wentelbaanpatrone, vertoon die kanaal 'n wisselende foutgedrag. Kommunikasievensters is beperk en moet geoptimeer word om die totale deurset van die stelsel te maksimeer. Groot koderingswinste kan verkry word deur die implementering van foutkorreksie kodes. Hierdie tesis voorsien 'n metode om die datadeurset van satelliete met lae wentelbaan te optimeer, deur middel van implementering van 'n missie-spesi eke foutbeheer strategie. Lae digtheid pariteit toetskodes (LDPC) is veelsydige kodes, bied goeie foutbeheer en is doeltre end vir verskillende kodekoerse en bloklengtes. Met drywingsbeperkinge op die ruimtesegment en afgesonderde grondstasies, moet hardeware komponente doeltreffend gebruik word om drywingsverbruik te verminder. Ten einde aan hierdie ontwerpsvereiste te voldoen, evalueer hierdie tesis verskeie LDPC dekodeerderalgoritmes. Deur 'n iteratiewe LDPC dekodeerder met 'n benaderingsalgoritme te implementeer, word 'n oplossing van lae kompleksiteit aangebied, maar wat steeds goeie foutkorreksie eienskappe toon. Die voorgestelde oplossing bied 'n baie goeie balans tussen benodigde hardeware kompleksiteit en koderingsprestasie. Daar is gevind dat heelwat parameters van die dekodeerders en kodes aangepas kan word, ten einde implementering in stelsels met 'n wye verskeidenheid van geheuespasie en verwerkingsvermoëns moontlik te maak.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A collaboration between the Katholieke Universiteit van Leuven (KUL) and Stellenbosch University (SU), resulted in the development of a satellite based platform for use in agricultural sensing applications. This will primarily serve as a test platform for a digitally beam-steerable antenna array (SAA) that was developed by KUL. SU developed all flight - and ground station based hardware and software, enabling ground to flight communications and interfacing with the KUL SAA. Although most components had already been completed at the start of this M:Sc:Eng: project, final systems integration was still unfinished. Modules necessary for communication were also outstanding. This project implemented an automatic repeat and request (ARQ) strategy for reliable file transfer across the wireless link. Channel coding has also been implemented on a field programmable gate array (FPGA). This layer includes an advanced forward error correction (FEC) scheme i.e. a low-density parity-check (LDPC), which outperforms traditional FEC techniques. A flexible architecture for channel coding has been designed that allows speed and complexity trade-offs on the FPGA. All components have successfully been implemented, tested and integrated. Simulations of LDPC on the FPGA have been shown to provide excellent error correcting performance. The prototype has been completed and recently successfully demonstrated at KUL. Data has been reliably transferred between the satellite platform and a ground station, during this event. / AFRIKAANSE OPSOMMING: Tydens ’n samewerkingsooreenkoms tussen die Katholieke Universiteit van Leuven (KUL) en die Universiteit van Stellenbosch (US) is ’n satelliet stelsel ontwikkel vir sensor-netwerk toepassings in die landbou bedryf. Hierdie stelsel sal hoofsaaklik dien as ’n toetsmedium vir ’n digitaal stuurbare antenna (SAA) wat deur KUL ontwikkel is. Die US het alle hardeware en sagteware komponente ontwikkel om kommunikasie d.m.v die SAA tussen die satelliet en ’n grondstasie te bewerkstellig. Sedert die begin van hierdie M:Sc:Ing: projek was die meeste komponente alreeds ontwikkel en geïmplementeer, maar finale stelselsintegrasie moes nog voltooi word. Modules wat kommunikasie sou bewerkstellig was ook nog uistaande. Hierdie projek het ’n ARQ protokol geïmplementeer wat data betroubaar tussen die satelliet en ’n grondstasie kon oordra. Kanaalkodering is ook op ’n veld programmeerbare hekskikking (FPGA) geïmplementeer. ’n Gevorderde foutkorrigeringstelsel, naamlik ’n lae digtheids pariteit toetskode (LDPC), wat tradisionele foutkorrigeringstelsels se doeltreffendheid oortref, word op hierdie FPGA geïmplementeer. ’n Kanaalkoderingsargitektuur is ook ontwikkel om die verwerkingspoed van data en die hoeveelheid FPGA logika wat gebruik word, teenoor mekaar op te weeg. Alle komponente is suksesvol geïmplementeer, getoets en geïntegreer met die hele stelsel. Simulasies van LDPC op die FPGA het uistekende foutkorrigeringsresultate gelewer. ’n Werkende prototipe is onlangs voltooi en suksesvol gedemonstreer by KUL. Betroubare data oordrag tussen die satelliet en die grondstasie is tydens hierdie demonstrasie bevestig.

Le multicast fiable est certainement la solution la plus efficace pour la distribution de contenu via un<br />tres grand nombre (potentiellement des millions) de recepteurs. Dans cette perspective les protocoles<br />ALC et FLUTE, standardises via l'IETF (RMT WG), ont ete adoptes dans 3GPP/MBMS et dans le<br />DVB-H IP-Datacast dans les contextes des reseaux cellulaires 3G.<br />Ce travail se concentre sur le multicast fiable et a comme requis principal le passage l'echelle massif<br />en terme de nombre de clients. Cette these se base sur les solutions proposees via l'IETF RMT WG.<br />Ces protocoles de multicast fiable sont construit autour de plusieurs briques de base que nous avons<br />etudie en detail:<br />* La brique Forward Error Correction (FEC) :<br />Nous examinons la classe de codes grands blocs Low Density Parity Check (LDPC). Nous concevons<br />des derivees de ces codes, et les analysons en detail. Nous en concluons que les codes<br />LDPC et leur implementation ont des performances tres prometteuses, surtout si ils sont utilisees<br />avec des fichiers de taille importante.<br />* La brique controle de congestion :<br />Nous examinons le comportement dans la phase de demarrage de trois protocoles de controle de<br />congestion RLC, FLID-SL, WEBRC. Nous demontrons que la phase de demarrage a un grand<br />impact sur les performances de telechargement.<br />Cette these a aussi plusieurs contributions au niveau applicatif:<br />* Extensions de FLUTE :<br />Nous proposons un mecanisme permettant d'agreger plusieurs fichiers dans le protocole FLUTE.<br />Ceci ameliore les performance de transmission.<br />* Streaming video :<br />Nous proposons SVSoA, une solution de streaming base sur ALC. Cette approche beneficie de<br />tout les avantages de ALC en terme de passage a l'echelle, controle de congestion et corrections<br />d'erreurs.<br /><br />Mots cles : Multicast fiable, FLUTE, ALC, codes correcteur d'erreurs, Forward Error Correction<br />(FEC), Low Density Parity Check (LDPC) Codes, diffusion de contenu