Capacity, coding and interference cancellation in multiuser multicarrier wireless communications systems

Multicarrier modulation and multiuser systems have generated a great deal of research during the last decade. Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation generated with the inverse Discrete Fourier Transform, which has been adopted for standards in wireless and wire-line communications. Multiuser wireless systems using multicarrier modulation suffer from the effects of dispersive fading channels, which create multi-access, inter-symbol, and inter-carrier interference (MAI, ISI, ICI). Nevertheless, channel dispersion also provides diversity, which can be exploited and has the potential to increase robustness against fading. Multiuser multi-carrier systems can be implemented using Orthogonal Frequency Division Multiple Access (OFDMA), a flexible orthogonal multiplexing scheme that can implement time and frequency division multiplexing, and using multicarrier code division multiple access (MC-CDMA). Coding, interference cancellation, and resource sharing schemes to improve the performance of multiuser multicarrier systems on wireless channels were addressed in this dissertation. Performance of multiple access schemes applied to a downlink multiuser wireless system was studied from an information theory perspective and from a more practical perspective. For time, frequency, and code division, implemented using OFDMA and MC-CDMA, the system outage capacity region was calculated for a correlated fading channel. It was found that receiver complexity determines which scheme offers larger capacity regions, and that OFDMA results in a better compromise between complexity and performance than MC-CDMA. From the more practical perspective of bit error rate, the effects of channel coding and interleaving were investigated. Results in terms of coding bounds as well as simulation were obtained, showing that OFDMAbased orthogonal multiple access schemes are more sensitive to the effectiveness of the code to provide diversity than non-orthogonal, MC-CDMA-based schemes. While cellular multiuser schemes suffer mainly from MAI, OFDM-based broadcasting systems suffer from ICI, in particular when operating as a single frequency network (SFN). It was found that for SFN the performance of a conventional OFDM receiver rapidly degrades when transmitters have frequency synchronization errors. Several methods based on linear and decision-feedback ICI cancellation were proposed and evaluated, showing improved robustness against ICI. System function characterization of time-variant dispersive channels is important for understanding their effects on single carrier and multicarrier modulation. Using time-frequency duality it was shown that MC-CDMA and DS-CDMA are strictly dual on dispersive channels. This property was used to derive optimal matched filter structures, and to determine a criterion for the selection of spreading sequences for both DS and MC CDMA. The analysis of multiple antenna systems provided a unified framework for the study of DS-CDMA and MC-CDMA on time and frequency dispersive channels, which can also be used to compare their performance

Estimation and detection techniques for doubly-selective channels in wireless communications

A fundamental problem in communications is the estimation of the channel. The signal transmitted through a communications channel undergoes distortions so that it is often received in an unrecognizable form at the receiver. The receiver must expend significant signal processing effort in order to be able to decode the transmit signal from this received signal. This signal processing requires knowledge of how the channel distorts the transmit signal, i.e. channel knowledge. To maintain a reliable link, the channel must be estimated and tracked by the receiver. The estimation of the channel at the receiver often proceeds by transmission of a signal called the 'pilot' which is known a priori to the receiver. The receiver forms its estimate of the transmitted signal based on how this known signal is distorted by the channel, i.e. it estimates the channel from the received signal and the pilot. This design of the pilot is a function of the modulation, the type of training and the channel. [Continues.

Décodage à seuil itératif des codes convolutionnels doublement orthogonaux perforés et application aux modulations multiniveaux

Éléments de théorie du codage -- Codes convolutionnels -- La technique de décodage turbo -- Décodage à seuil itératif et codage convolutionnel doublement orthogonal -- Forces et faiblesses du décodage turbo -- Décodage à seuil et codes convolutionnels orthogonaux -- Décodage à seuil itératif et codes convolutionels doublement orthogonaux -- Perforation des codes doublement orthogonaux -- Influence de la perforation des CSO2C-WS sur les performances du décodage à seuil itératif -- Propriétés des PCS)"C-WS -- Application aux modulations à erfficacités spectrales élevées -- Introduction aux modulations numériques -- Assignation des symboles de canal aux signaux de la constellation par codage de Gray -- Performances du décodage à seuil itératif avec assignation par codage de Gray -- Assignation par partition d'ensemble -- Utilisation de l'assignation par partition d'ensemble dans le cas de PCSO2C non optimaux

Coding Theory

Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete mathematics and combinatorics, complexity theory, and statistical physics. The workshop on coding theory covered many facets of the recent research advances

Conception et prototypage de décodeurs à seuil itératif à haut débit

Codage de canal -- Système de communication numérique -- Principe du codage correcteur d'erreur -- Les codes LDPC -- Les codes Turbo -- Les codes CDO -- Notions matérielles -- La technologie FPGA -- Les FPGA de la famille Virtex-II pro de Xilinx -- Délai critique d'un circuit numérique -- Stratégie de resynchronisation d'un circuit numérique -- Environnement d'évaluation des performances d'erreur du DSI -- Décodeur à seuil itératif à haut débit des codes CDO -- Architecture du décodeur à seuil -- Le pondérateur -- Les registres à décalage -- Technique de pipelinage du décodeur -- Stratégie de resynchronisation du décodeur -- Emplacements des étages de pipeline -- Capacité de pipelinage d'un codeur CDO -- Implémentation des composants pipelinés -- Système de communication adapté aux codes perforés -- Gestionnaire d'horloge -- Endoceur perforé -- Décodeur à seuil itératif adapté aux codes perforés -- Recherche de générateurs des codes PCDO à taux compatibles et à haute capacité de pipelinage -- Codes convolutionnels doublement orthogonaux à multi-registres à décalage -- Définition des codes M-CDO -- Simplification des codes M-CDO -- Représentation vectorielle des différences simples et doubles -- Simplification des conditions de la définition des codes M-CDO -- Décodeur à seuil itératif à haut débit de codes M-CDO -- Les registres à décalage -- Le noyau de logique combinatoire -- Pipelinage du décodeur à seuil des codes M-CDO -- Nombre d'emplacements des étages de pipeline -- Capacité de pipelinage d'un générateur de codes M-CDO -- Recherche des meilleurs générateurs de codes M-CDO -- Notations utilisées -- Comparaison des délais des deux architectures du pondérateur -- Choix de la résolution interne du décodeur -- Pipelinage du décodeur à seuil -- Influence de l'architecture du registre à décalage élémentaire -- Exemple de pipelinage d'un décodeur à seuil des codes M-CPDO -- Prototypage du DSI des codes PCDO à taux compatibles -- Simulation du gestionnaire d'horloge -- Résultats expérimentaux du DSI des codes PCDO à taux compatibles -- Influence de la potection quasi-EEP sur les performances -- Comparaison des codes doublement orthogonaux

Quantum two-block group algebra codes

We consider quantum two-block group algebra (2BGA) codes, a previously unstudied family of smallest lifted-product (LP) codes. These codes are related to generalized-bicycle (GB) codes, except a cyclic group is replaced with an arbitrary finite group, generally non-abelian. As special cases, 2BGA codes include a subset of square-matrix LP codes over abelian groups, including quasi-cyclic codes, and all square-matrix hypergraph-product codes constructed from a pair of classical group codes. We establish criteria for permutation equivalence of 2BGA codes and give bounds for their parameters, both explicit and in relation to other quantum and classical codes. We also enumerate the optimal parameters of all inequivalent connected 2BGA codes with stabilizer generator weights $W \le 8$, of length $n \le 100$ for abelian groups, and $n \le 200$ for non-abelian groups.Comment: 19 pages, 9 figures, 3 table

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

A STUDY OF LINEAR ERROR CORRECTING CODES

Since Shannon's ground-breaking work in 1948, there have been two main development streams of channel coding in approaching the limit of communication channels, namely classical coding theory which aims at designing codes with large minimum Hamming distance and probabilistic coding which places the emphasis on low complexity probabilistic decoding using long codes built from simple constituent codes. This work presents some further investigations in these two channel coding development streams. Low-density parity-check (LDPC) codes form a class of capacity-approaching codes with sparse parity-check matrix and low-complexity decoder Two novel methods of constructing algebraic binary LDPC codes are presented. These methods are based on the theory of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, and are complementary to each other. The two methods generate in addition to some new cyclic iteratively decodable codes, the well-known Euclidean and projective geometry codes. Their extension to non binary fields is shown to be straightforward. These algebraic cyclic LDPC codes, for short block lengths, converge considerably well under iterative decoding. It is also shown that for some of these codes, maximum likelihood performance may be achieved by a modified belief propagation decoder which uses a different subset of 7^ codewords of the dual code for each iteration. Following a property of the revolving-door combination generator, multi-threaded minimum Hamming distance computation algorithms are developed. Using these algorithms, the previously unknown, minimum Hamming distance of the quadratic residue code for prime 199 has been evaluated. In addition, the highest minimum Hamming distance attainable by all binary cyclic codes of odd lengths from 129 to 189 has been determined, and as many as 901 new binary linear codes which have higher minimum Hamming distance than the previously considered best known linear code have been found. It is shown that by exploiting the structure of circulant matrices, the number of codewords required, to compute the minimum Hamming distance and the number of codewords of a given Hamming weight of binary double-circulant codes based on primes, may be reduced. A means of independently verifying the exhaustively computed number of codewords of a given Hamming weight of these double-circulant codes is developed and in coiyunction with this, it is proved that some published results are incorrect and the correct weight spectra are presented. Moreover, it is shown that it is possible to estimate the minimum Hamming distance of this family of prime-based double-circulant codes. It is shown that linear codes may be efficiently decoded using the incremental correlation Dorsch algorithm. By extending this algorithm, a list decoder is derived and a novel, CRC-less error detection mechanism that offers much better throughput and performance than the conventional ORG scheme is described. Using the same method it is shown that the performance of conventional CRC scheme may be considerably enhanced. Error detection is an integral part of an incremental redundancy communications system and it is shown that sequences of good error correction codes, suitable for use in incremental redundancy communications systems may be obtained using the Constructions X and XX. Examples are given and their performances presented in comparison to conventional CRC schemes