Les systèmes de téléphonie mobile de 4ème et 5ème générations ont adopté comme techniques de codage de canal les turbocodes, les codes LDPC et les codes polaires binaires. Cependant, ces codes ne permettent pas de répondre aux exigences, en termes d’efficacité spectrale et de fiabilité, pour les réseaux de communications futurs (2030 et au-delà), qui devront supporter de nouvelles applications telles que les communications holographiques, les véhicules autonomes, l’internet tactile … Un premier pas a été fait il y a quelques années vers la définition de codes correcteurs d’erreurs plus puissants avec l’étude de codes LDPC non binaires, qui ont montré une meilleure performance que leurs équivalents binaires pour de petites tailles de code et/ou lorsqu'ils sont utilisés sur des canaux non binaires. En contrepartie, les codes LDPC non binaires présentent une complexité de décodage plus importante que leur équivalent binaire. Des études similaires ont commencé à émerger du côté des turbocodes. Tout comme pour leurs homologues LDPC, les turbocodes non binaires présentent d’excellentes performances pour de petites tailles de blocs. Du point de vue du décodage, les turbocodes non binaires sont confrontés au même problème d’augmentation de la complexité de traitement que les codes LDPC non binaire. Dans cette thèse nous avons proposé une nouvelle structure de turbocodes non binaires en optimisant les différents blocs qui la constituent. Nous avons réduit la complexité de ces codes grâce à la définition d’un algorithme de décodage simplifié. Les codes obtenus ont montré des performances intéressantes en comparaison avec les codes correcteur d’erreur de la littérature. / Nowadays communication standards have adopted different binary forward error correction codes. Turbo codes were adopted for the long term evolution standard, while binary LDPC codes were standardized for the fifth generation of mobile communication (5G) along side with the polar codes. Meanwhile, the focus of the communication community is shifted towards the requirement of beyond 5G standards. Networks for the year 2030 and beyond are expected to support novel forward-looking scenarios, such as holographic communications, autonomous vehicles, massive machine-type communications, tactile Internet… To respond to the expected requirements of new communication systems, non-binary LDPC codes were defined, and they are shown to achieve better error correcting performance than the binary LDPC codes. This performance gain was followed by a high decoding complexity, depending on the field order.Similar studies emerged in the context of turbo codes, where the non-binary turbo codes were defined, and have shown promising error correcting performance, while imposing high complexity. The aim of this thesis is to propose a new low-complex structure of non-binary turbocodes. The constituent blocks of this structure were optimized in this work, and a new low complexity decoding algorithm was proposed targeting a future hardware implementation. The obtained results are promising, where the proposed codes are shown to outperform existing binary and non-binary codes from the literature.

<p>Turbo codes was first presented in 1993 by C. Berrou, A. Glavieux and P. Thitimajshima. Since then this class of error correcting codes has become one of the most popular, because of its good properties. The turbo codes are able to come very close to theoretical limit, the Shannon limit. Turbo codes are for example used in the third generation of mobile phone (3G) and in the standard IEEE 802.16 (WiMAX).</p><p>There are some drawbacks with the algorithm for decoding turbo codes. The deocoder uses a Maximum A Posteriori (MAP) algorithm, which is a complex algorith. Because of the use of many variables in the decoder the decoding circuit will consume a lot of power due to memory accesses and internal communication. One way in which this can be reduced is to make early decisions.</p><p>In this work I have focused on making early decision of the encoder states. One major part of the work was also to be sure that the expressions were written in a way that as few variables as possible are needed. A termination condition is also introduced. Simulations based on estimations of the number of memory accesses, shows that the number of memory accesses will significantly decrease.</p>

Turbo codes was first presented in 1993 by C. Berrou, A. Glavieux and P. Thitimajshima. Since then this class of error correcting codes has become one of the most popular, because of its good properties. The turbo codes are able to come very close to theoretical limit, the Shannon limit. Turbo codes are for example used in the third generation of mobile phone (3G) and in the standard IEEE 802.16 (WiMAX). There are some drawbacks with the algorithm for decoding turbo codes. The deocoder uses a Maximum A Posteriori (MAP) algorithm, which is a complex algorith. Because of the use of many variables in the decoder the decoding circuit will consume a lot of power due to memory accesses and internal communication. One way in which this can be reduced is to make early decisions. In this work I have focused on making early decision of the encoder states. One major part of the work was also to be sure that the expressions were written in a way that as few variables as possible are needed. A termination condition is also introduced. Simulations based on estimations of the number of memory accesses, shows that the number of memory accesses will significantly decrease.

Orientador: Celso de Almeida / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-12T06:34:19Z (GMT). No. of bitstreams: 1 Mataveli_LuisOtavio_M.pdf: 877476 bytes, checksum: afc5fb9153e7311af03669d45d798a73 (MD5) Previous issue date: 2008 / Resumo: O desempenho dos sistemas de comunicação sem fio que utilizam a técnica de múltiplo acesso CDMA é limitado pela interferência. A proposição de um algoritmo de escolha de seqüências de espalhamento foi feita para buscar uma diminuição na interferência média do sistema. Nos padrões atuais, como CDMA2000 e WCDMA, não são definidos nenhum critério para escolha das seqüências. Por isso, nesta dissertação será analisado o desempenho do algoritmo de escolha de seqüências de espalhamento proposto anteriormente juntamente com o uso de códigos corretores de erro em canais com desvanecimento seletivo em freqüência. Será analisado o comportamento das seqüências Walsh, Gold e m-deslocadas. O algoritmo analisado apresenta bons resultados sem o uso de codificação, mas, como maneira de analisar um sistema mais próximo do real, serão utilizados os códigos convolucionais e turbo. Palavras-chave: Algoritmo de busca, sistemas CDMA, espalhamento espectral, códigos convolucionais, códigos turbo. / Abstract: The performance of wireless communication systems that use the multiple access code division technique, CDMA, is interference-limited. A sequence selection algorithm allows a reduction in the mean interference of the system. In the standards like CDMA2000 and WCDMA no algorithm is defined for choosing the sequences. For this reason, in this dissertation we evaluate the performance of the proposed spread sequences selection algorithm together with error correcting codes over frequency selective fading channels. It is analyzed the behavior of Walsh, Gold, and shifted-m sequences. The algorithm had shown good results without channel coding, but to analyze a system similar to a real one, convolutional and turbo codes are going to be used. Key words: Selection algorithm, CDMA systems, spread spectrum, convolutional codes, turbo codes. / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica

The aim is to explain the Turbo convolutional and block turbo codes and decoding the secure message. The practical part focuses on the design of a demonstration program in Matlab. The work is divided into four parts. The first two deal with theoretical analysis of coding and decoding. The third section contains a description created a demonstration program that allows you to navigate the process of encoding and decoding. The fourth is devoted to simulation and performance of turbo codes.

No description available.

Un code correcteur d'erreur ajoute de la redondance à un message afin de pouvoir corriger celui-ci lorsque des erreurs se sont introduites pendant la transmission. Les codes convolutifs sont des codes performants, et par conséquent, souvent utilisés. Le principe d'un code convolutif consiste à se fixer une fonction de transfert définie sur le groupe des entiers relatifs et à effectuer la convolution d'un message avec cette fonction de transfert. Ces codes ne protègent pas le message d'une interception par une tierce personne. C'est pourquoi nous proposons dans cette thèse, des codes convolutifs avec des propriétés cryptographiques, définis sur des groupes non-commutatifs. Nous avons tout d'abord étudié les codes définis sur le groupe diédral infini, qui, malgré de bonnes performances, n'ont pas les propriétés cryptographiques recherchées. Nous avons donc étudié ensuite des codes convolutifs en bloc sur des groupes finis, avec un encodage variable dans le temps. Nous avons encodé chaque message sur un sous-ensemble du groupe différent à chaque encodage. Ces sous-ensembles sont générés de façon chaotique à partir d'un état initial, qui est la clé du cryptosystème symétrique induit par le code. Nous avons étudié plusieurs groupes et plusieurs méthodes pour définir ces sous-ensembles chaotiques. Nous avons étudié la distance minimale des codes que nous avons conçus et montré qu'elle est légèrement plus petite que la distance minimale des codes en blocs linéaires. Cependant, nous avons, en plus, un cryptosystème symétrique associé à ces codes. Ces codes convolutifs non-commutatifs sont donc un compromis entre correction d'erreur et sécurité. / An error correcting code adds redundancy to a message in order to correct it when errors occur during transmission.Convolutional codes are powerful ones, and therefore, often used. The principle of a convolutional code is to perform a convolution product between a message and a transfer function, both defined over the group of integers. These codes do not protect the message if it is intercepted by a third party. That is why we propose in this thesis, convolutional codes with cryptographic properties defined over non-commutative groups. We first studied codes over the infinite dihedral group, which despite good performance, do not have the desired cryptographic properties. Consequently, we studied convolutional block codes over finite groups with a time-varying encoding. Every time a message needs to be encoded, the process uses a different subset of the group. These subsets are chaotically generated from an initial state. This initial state is considered as the symmetric key of the code-induced cryptosystem. We studied many groups and many methods to define these chaotic subsets. We examined the minimum distance of the codes we conceived and we showed that it is slightly smaller than the minimum distance of the linear block codes. Nevertheless, our codes have, in addition, cryptographic properties that the others do not have. These non-commutative convolutional codes are then a compromise between error correction and security.

We compare LDPC block and LDPC convolutional codes with respect to their decoding performance under low decoding latencies. Protograph based regular LDPC codes are considered with rather small lifting factors. LDPC block and convolutional codes are decoded using belief propagation. For LDPC convolutional codes, a sliding window decoder with different window sizes is applied to continuously decode the input symbols. We show the required Eb/N0 to achieve a bit error rate of 10 -5 for the LDPC block and LDPC convolutional codes for the decoding latency of up to approximately 550 information bits. It has been observed that LDPC convolutional codes perform better than the block codes from which they are derived even at low latency. We demonstrate the trade off between complexity and performance in terms of lifting factor and window size for a fixed value of latency. Furthermore, the two codes are also compared in terms of their complexity as a function of Eb/N0. Convolutional codes with Viterbi decoding are also compared with the two above mentioned codes.

We compare LDPC block and LDPC convolutional codes with respect to their decoding performance under low decoding latencies. Protograph based regular LDPC codes are considered with rather small lifting factors. LDPC block and convolutional codes are decoded using belief propagation. For LDPC convolutional codes, a sliding window decoder with different window sizes is applied to continuously decode the input symbols. We show the required Eb/N0 to achieve a bit error rate of 10 -5 for the LDPC block and LDPC convolutional codes for the decoding latency of up to approximately 550 information bits. It has been observed that LDPC convolutional codes perform better than the block codes from which they are derived even at low latency. We demonstrate the trade off between complexity and performance in terms of lifting factor and window size for a fixed value of latency. Furthermore, the two codes are also compared in terms of their complexity as a function of Eb/N0. Convolutional codes with Viterbi decoding are also compared with the two above mentioned codes.