Turbo codes are a new class of codes that can achieve exceptional error performance and energy efficiency at low signal-to-noise ratios. Decoding turbo codes is a complicated procedure that often requires custom hardware if it is to be performed at acceptable speeds. Configurable computing machines are able to provide the performance advantages of custom hardware while maintaining the flexibility of general-purpose microprocessors and DSPs. This thesis presents an implementation of a turbo decoder on an FPGA-based configurable computing platform. Portability and flexibility are emphasized in the implementation so that the decoder can be used as part of a configurable software radio. The system presented performs turbo decoding for a variable block size with a variable number of decoding iterations while using only a single FPGA. When six iterations are performed, the decoder operates at an information bit rate greater than 32 kbps. / Master of Science

[pt] Códigos turbo são uma técnica de correção de erro eficiente que vem sendo proposta em diversos padrões de comunicações atuais. Esta técnica apresenta um desempenho que se aproxima dos limites teóricos estabelecidos na Teoria de Codificação. A razão para o excelente desempenho deste tipo de código baseia-se em dois fatores: uma estrutura de codificação composta por codificadores concatenados e uma estrutura de decodificação iterativa. Neste trabalho é realizada uma revisão da literatura onde a decodificação turbo é discutida segundo duas abordagens: uma que baseia-se na estrutura dos codificadores empregados e outra baseada na moderna teoria de grafos- fatores. O desempenho destes códigos é avaliado através de simulações. São considerados fatores como a estrutura dos codificadores, o tipo de modulação empregada, o algoritmo de decodificação utilizado, entre outros. / [en] Turbo codes are an efficient error correcting technique that has been proposed for many communications standards. This technique achieves a performance that is near the theoretical limits established by Information Theory. The reason for this excellent performance of turbo codes relies on two aspects: a coding structure that is composed by concatenated encoders and an iterative decoding procedure. In the literature, two approaches for turbo decoding are presented: one that is based on the encoder structure and another that is built around the factor graphs theory. Both approaches are discussed in this work. Performance evaluation for these codes are obtained through simulations. Some aspects such as encoder structure, modulation scheme and decoding algorithm are considered and evaluated. Also codes derived from turbo codes by puncturing and shortening have been studied in this work.

Cet exposé analyse les perspectives large bande des réseaux PMR, à travers l'évaluation du candidat LTE, et la proposition d'une possible évolution du codage canal, la solution brevetée des codes turbo à protection non uniforme. Une première étude dans le chapitre 2 se concentre sur l'analyse multi-couche et l'identification des problèmes clé des communications de voix et de vidéo sur un réseau LTE professionnel. Les capacités voix et vidéo sont estimées pour les liens montant et descendant de la transmission LTE, et l'efficacité spectrale de la voix en lien descendant est comparée à celle de PMR et GSM. Ce chapitre souligne certains points clé de l'évolution de LTE. S'ils étaient pas résolus par la suite, LTE se verrait perdre de sa crédibilité en tant que candidat à l'évolution de la PMR. Une telle caractéristique clé des réseaux PMR est le codage canal à protection non uniforme, qui pourrait être adapté au système LTE pour une évolution aux contraintes de la sécurité publique. Le chapitre 3 introduit cette proposition d'évolution, qui a été brevetée: les turbo codes à protection non uniforme intégrée. Nous proposons une nouvelle approche pour le codage canal à protection non uniforme à travers les codes turbo progressives hiérarchiques. Les configurations parallèles et séries sont analysées. Les mécanismes de protection non uniformes sont intégrés dans la structure de l'encodeur même à travers l'insertion progressif et hiérarchique de nouvelles données de l'utilisateur. Le turbo décodage est modifié pour exploiter de façon optimale l'insertion progressive de données dans le processus d'encodage et estimer hiérarchiquement ces données. Les propriétés des structures parallèles et séries sont analysées à l'aide d'une analogie aux codes pilotes, ainsi qu'en regardant de plus près leurs caractéristiques de poids de codage. Le taux de transmission virtuel et les représentations des graphs factor fournissent une meilleure compréhension de ces propriétés. Les gains de codage sont évalués à l'aide de simulations numériques, en supposant des canaux de transmission radio statiques et dynamiques, et en utilisant des codes de référence. Enfin, dans le chapitre 4, l'idée breveté du code turbo parallal progressif et hiérarchique (PPHTC) est évaluée sur la plateforme LTE. Une description détaillée de l'architecture des bearers de LTE est donnée, et ses conséquences sont discutées. Le nouveau codage canal est inséré et évalué sur cette plateforme, et ses performances sont comparées avec des schémas de transmission typique à LTE. L'analyse de la qualité de la voix aide à conclure sur l'efficacité de la solution proposée dans un système de transmission réel. Pourtant, même si cette dernière donne les meilleurs résultats, d'avantage d'optimisations devraient être envisagées pour obtenir des gains améliorés et mieux exploiter le potentiel du codage proposé. L'exposé se conclut dans le chapitre 5 et une courte discussion présente les futures perspectives de recherche / This dissertation analyzes the PMR broadband perspectives, through the evaluation of the preferred candidate, LTE, and the proposal of a possible channel coding evolution, the patented solution of unequal error protection embedded turbo codes. A first study in chapter 2 focuses on the multi-layer analysis and the identification of key issues for professional-like LTE for voice and video communications. The voice and video capacities are estimated for both downlink and uplink LTE transmissions, and the downlink LTE voice system efficiency is compared with that of the PMR and Global System for Mobile Communications (GSM). This chapter helps highlighting some of the key points. If not resolved, the latter could lead to the LTE downfall as a candidate for the PMR evolution. One such key characteristic of PMR systems is the unequal error protection channel coding technique, which might be adapted to the LTE technology for its evolution to public safety requirements. Chapter 3 further introduces the proposed evolution patented ideas: the unequal error protection embedded turbo codes. We propose a new approach for the unequal error protection channel coding through the progressive hierarchical turbo codes. Both parallel and serial turbo configurations are closely studied. The unequal error protection mechanisms are embedded in the encoder’s structure itself through the progressive and hierarchical insertion of new data. The turbo decoding is modified as to optimally exploit the progressive insertion of information in the encoding process and hierarchically estimate the corresponding data. Both parallel and serial configurations’ properties are analyzed using an analogy with a pilot code behavior, as well as a zoom on the weight error functions coefficients. The virtual code rate and factor graph interpretations also provide a better insight on the code properties. The code possible gains are highlighted through computer simulations in both static and dynamic transmission environments, by using carefully chosen benchmarks. Finally, in chapter 4, the patented idea of parallel progressive hierarchical turbo codes (PPHTC) is evaluated over the LTE platform. A detailed description is given of the voice transmission bearer architecture over LTE, and its consequences are discussed. The new channel code is inserted and evaluated over this platform and its performances compared with the existent LTE transmission schemes. The voice quality results help concluding on the efficiency of the proposed solution in a real transmission scenario. However, even though the newly presented solution gives the best results, further system optimizations should be envisaged for obtaining better gains and exploit the parallel progressive hierarchical turbo codes potential. The dissertation concludes in chapter 5 and a short discussion is given on future research perspectives

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / A study of the effects of interference caused by adjacent channels on the performance of turbo-coded 16- and 32-APSK. Included in our discussion is the spectral regrowth in the nonlinear power amplifier when driven by a non-constant envelope modulation. Ultimately, we present a set of channel spacing guidelines when using turbo-coded APSK for aeronautical telemetry.

Turbo códigos têm se tornado um importante ramo na pesquisa de codificação de canal e já foram adotados como padrão para a terceira geração de comunicação móvel. Devido ao seu alto ganho de codificação, os turbo códigos são vistos como fortes candidatos a serem adotados como padrão das futuras gerações de redes sem fio. Esse esquema de codificação é baseado na decodificação iterativa, onde decodificadores de entrada e saída suaves produzem refinamento da informação a cada iteração. Essa dissertação apresenta resultados de um estudo comparativo entre dois esquemas de codificação: turbo códigos de bloco e turbo códigos convolucionais. Os resultados mostram que os dois esquemas de codificação têm desempenho funcional complementar, sendo importante a especificação de um alvo em termos de relação sinal/ruído ou taxa de erro de bits para a escolha do esquema de codificação mais adequado. Com o mesmo modelo em linguagem de programação C foi feita uma exploração do algoritmo visando diminuição do consumo de potência. Essa exploração em parte foi feita segundo uma metodologia de exploração sistemática das possibilidades de transferência e armazenamento de dados (DTSE). Com a exploração, a redução total de consumo de potência para o armazenamento de dados foi estimada em 34%. / Turbo codes have become an important branch on channel coding research and have been adopted as standard in the third generation of mobile communication systems. Due to their high coding gain, turbo codes are expected to be part of the next generations of wireless networks standards. This coding scheme is based on iterative decoding, as soft input/soft output decoders produce an information refinement in each iteration. This dissertation shows the results of a comparative performance study of two different turbo coding schemes: block turbo codes and convolutional turbo codes. The results obtained show that the two schemes have complementary performance. It is necessary to specify a target in terms of bit error rate or signal/noise ratio. With the same C model an exploration aiming at reducing power consumption was done. Part of this exploration was done following a systematic methodology of data transfer and storage exploration (DTSE). With this exploration, a reduction of 34% on power consumption was estimated.

Turbo códigos têm se tornado um importante ramo na pesquisa de codificação de canal e já foram adotados como padrão para a terceira geração de comunicação móvel. Devido ao seu alto ganho de codificação, os turbo códigos são vistos como fortes candidatos a serem adotados como padrão das futuras gerações de redes sem fio. Esse esquema de codificação é baseado na decodificação iterativa, onde decodificadores de entrada e saída suaves produzem refinamento da informação a cada iteração. Essa dissertação apresenta resultados de um estudo comparativo entre dois esquemas de codificação: turbo códigos de bloco e turbo códigos convolucionais. Os resultados mostram que os dois esquemas de codificação têm desempenho funcional complementar, sendo importante a especificação de um alvo em termos de relação sinal/ruído ou taxa de erro de bits para a escolha do esquema de codificação mais adequado. Com o mesmo modelo em linguagem de programação C foi feita uma exploração do algoritmo visando diminuição do consumo de potência. Essa exploração em parte foi feita segundo uma metodologia de exploração sistemática das possibilidades de transferência e armazenamento de dados (DTSE). Com a exploração, a redução total de consumo de potência para o armazenamento de dados foi estimada em 34%. / Turbo codes have become an important branch on channel coding research and have been adopted as standard in the third generation of mobile communication systems. Due to their high coding gain, turbo codes are expected to be part of the next generations of wireless networks standards. This coding scheme is based on iterative decoding, as soft input/soft output decoders produce an information refinement in each iteration. This dissertation shows the results of a comparative performance study of two different turbo coding schemes: block turbo codes and convolutional turbo codes. The results obtained show that the two schemes have complementary performance. It is necessary to specify a target in terms of bit error rate or signal/noise ratio. With the same C model an exploration aiming at reducing power consumption was done. Part of this exploration was done following a systematic methodology of data transfer and storage exploration (DTSE). With this exploration, a reduction of 34% on power consumption was estimated.

Dans le cadre de cette thèse nous nous intéressons à la liaison d'un terminal utilisateur vers un satellite géostationnaire pour les futurs systèmes d'applications multimédia en bande Ka. Le but est de concevoir une forme d'onde qui permet de s'adapter aux conditions de propagation. L'adaptation des performances en spectre et en puissance de la forme d'onde, notamment dans un contexte avec une forte fluctuation du niveau du signal, comme celui du canal satellite en bande Ka, permet à la fois d'augmenter la capacité et d'améliorer la disponibilité du système. Dans ces travaux, les formes d'onde basées sur les modulations CPM (Continuous Phase Modulation) ont été adoptées. L'enveloppe constante, les différents paramètres ayant un impact sur les performances de la forme d'onde, ainsi que les bonnes performances en puissance lors d'un processus de décodage itératif sont les principales motivations de notre choix. Concernant l'adaptativité nous montrons qu'une forme d'onde CPM basée sur la variation de l'indice de modulation (et éventuellement la réponse en fréquence) au sein d'une famille d'indices ayant un même dénominateur est une solution particulièrement attractive. Une telle solution ne nécessite pas une très grande complexité lors d'un passage d'un mode de transmission à un autre. Elle nécessite essentiellement le changement des coefficients des filtres adaptés. Cette technique permet aussi d'obtenir une marge de performance assez importante vu que l'indice de modulation est le paramètre qui affecte le plus les performances de la CPM. La CPM octale 2RC est un schéma particulièrement attractif d'un point de vue performance.

Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

Battail [1989] shows that an appropriate criterion for the design of long block codes is the closeness of the normalized weight distribution to a Gaussian distribution. A subsequent work shows that iterated product of single parity check codes satisfy this criterion [1994]. Motivated by these earlier works, in this thesis, we study the effect of the interleaver on the performance of turbo codes for large block lengths, $N\rightarrow\infty$. A parallel concatenated turbo code that consists of two or more component codes is considered. We demonstrate that for $N\rightarrow\infty$, the normalized weight of the systematic $\widehat{w_1}=\displaystyle\frac{w_1}{\sqrt{N}}$, and the parity check sequences $\widehat{w_2}=\displaystyle\frac{w_2}{\sqrt{N}}$ and $\widehat{w_3}=\displaystyle\frac{w_3}{\sqrt{N}}$ become a set of jointly Gaussian distributions for the typical values of $\widehat{w_i},i=1,2,3$, where the typical values of $\widehat{w_i}$ are defined as $\displaystyle\lim_{N\rightarrow\infty}\frac{\widehat{w_i}}{\sqrt{N}}\neq 0,1$ for $i=1,2,3$. To optimize the turbo code performance in the waterfall region which is dominated by high-weight codewords, it is desirable to reduce $\rho_{ij}$, $i,j=1,2,3$ as much as possible, where $\rho_{ij}$ is the correlation coefficient between $\widehat{w_i}$ and $\widehat{w_j}$. It is shown that: (i)~$\rho_{ij}>0$, $i,j=1,2,3$, (ii)~$\rho_{12},\rho_{13}\rightarrow 0$ as $N\rightarrow\infty$, and (iii)~$\rho_{23}\rightarrow 0$ as $N\rightarrow\infty$ for "almost" any random interleaver. This indicates that for $N\rightarrow\infty$, the optimization of the interleaver has a diminishing effect on the distribution of high-weight error events, and consequently, on the error performance in the waterfall region. We show that for the typical weights, this weight distribution approaches the average spectrum defined by Poltyrev [1994]. We also apply the tangential sphere bound (TSB) on the Gaussian distribution in AWGN channel with BPSK signalling and show that it performs very close to the capacity for code rates of interest. We also study the statistical properties of the low-weight codeword structures. We prove that for large block lengths, the number of low-weight codewords of these structures are some Poisson random variables. These random variables can be used to evaluate the asymptotic probability mass function of the minimum distance of the turbo code among all the possible interleavers. We show that the number of indecomposable low-weight codewords of different types tend to a set of independent Poisson random variables. We find the mean and the variance of the union bound in the error floor region and study the effect of expurgating low-weight codewords on the performance. We show that the weight distribution in the transition region between Poisson and Gaussian follows a negative binomial distribution. We also calculate the interleaver gain for multi-component turbo codes based on these Poisson random variables. We show that the asymptotic error performance for multi-component codes in different weight regions converges to zero either exponentially (in the Gaussian region) or polynomially (in the Poisson and negative binomial regions) with respect to the block length, with the code-rate and energy values close to the channel capacity.

A low-complexity method of interleaver design, sub-vector interleaving, for both parallel and serially concatenated convolutional codes (PCCCs and SCCCs, respectively) is presented here. Since the method is low-complexity, it is uniquely suitable for designing long interleavers. Sub-vector interleaving is based on a dynamical system representation of the constituent encoders employed by PCCCs and SCCCs. Simultaneous trellis termination can be achieved with a single tail sequence using sub-vector interleaving for both PCCCs and SCCCs. In the case of PCCCs, the error floor can be lowered by sub-vector interleaving which allows for an increase in the weight of the free distance codeword and the elimination of the lowest weight codewords generated by weight-2 terminating input sequences that determine the error floor at low signal-to-noise ratios (SNRs). In the case of SCCCs, sub-vector interleaving lowers the error floor by increasing the weight of the free distance codewords. Interleaver gain can also be increased for SCCCs by interleaving the lowest weight codewords from the outer into non-terminating input sequences to the inner encoder. Sub-vector constrained S-random interleaving, a method for incorporating S-random interleaving into sub-vector interleavers, is also proposed. Simulations show that short interleavers incorporating S-random interleaving into sub-vector interleavers perform as well as or better than those designed by the best and most complex methods for designing short interleavers. A method for randomly generating sub-vector constrained S-random interleavers that maximizes the spreading factor, S, is also examined. The convergence of the turbo decoding algorithm to maximum-likelihood decisions on the decoded input sequence is required to demonstrate the improvement in BER performance caused by the use of sub-vector interleavers. Convergence to maximum-likelihood decisions by the decoder do not always occur in the regions where it is feasible to generate the statistically significant numbers of error events required to approximate the BER performance for a particular coding scheme employing a sub-vector interleaver. Therefore, a technique for classifying error events by the mode of convergence of the decoder is used to illuminate the effect of the sub-vector interleaver at SNRs where it is possible to simulate the BER performance of the coding scheme.