Conventionally, the free distance is taken as the principle criterion for computing the error of convolutional and linear block codes. In other words, a larger free distance implies a better correction ability for the error correction codes. Distance spectrum is also an important factor for Maximum likelihood decoding. In this thesis, distance spectrum for different convolutional codes and CPM systems are investigated by us. Experiments results has demonstrate that a better correction ability of a shorter free distance does exist in some cases if they have a better distance spectrum. We also improve the fast algorithm for computing the distance spectrum developed by M. Cedervall and R. Johannesson. Their success is based upon the strategy of a traveling along the coding tree to find the distance spectrum. However, they need a new traveling for ever new distance computation. In contrast, we compute all the distance spectrum just in one travel by taking the advantage of the storing nodes of previous distance computation.

Combined coding with modulation is an important topic. It is verified in this thesis that a combined decoder and demodulation Viterbi receiver has a better error probability than a cascade of two separate Viterbi decoder and demodulator. Conventionally, the free distance is taken as the principle criterion for computing the error probability for coding or modulation. In many cases, distance spectrum needs to be provided for analyze the Maximum likelihood decoding. However, it is difficult for computing the distance spectrum for a combined coding with modulation because of a nonlinear structure inside. In this thesis, we first build an augmented trellis for the combined coding with modulation. Applying the concept of difference by exclusive OR and regular subtraction to the augmented trellis, we build an improved virtual trellis. As a consequence the distance spectrum for our problem can be computed because of the linear structure of the virtual trellis. The distance spectrum for different convolutional codes and CPM systems are investigated by us. Experiments results have demonstrate that a better distance spectrum implies a better error ability.

Combined coding with modulation is an important topic. Conventionally, the free distance is taken as the principle criterion for computing the error probability for coding or modulation. In many cases, distance spectrum needs to be provided for analyze the Maximum likelihood decoding. However, it is difficult for computing the distance spectrum for a combined coding with modulation because of a nonlinear structure inside. In this thesis, we study the order of distance spectrum members to find some limited number of members to present the whole distance spectrum. In our previous work, we have built an augmented trellis for the combined coding with modulation. Applying the concept of difference by exclusive OR and regular subtraction to the augmented trellis, we build an improved virtual trellis. In this thesis, we expend the concept of subtraction to a pair relation. Thus, this augmented trellis is first composed of paired states and transition lines. Then, we use a partition principle to group the states and lines. Finally, the complex trellis is reduced to a reasonable structure. We therefore can apply distance spectrum computing algorithm to find the distance spectrum. The distance spectrum for different convolution codes and CPM systems are investigated by us. Experiments results have demonstrate this distance spectrum is more accurate than before.

In this thesis, we compute the distance spectrum for non-causal generating signals and compare the different spectrum effects for different non-causal systems. The non-causal system is the system which the present output is determined by the future and the past. The distance spectrum is the list of the difference measures of any two signals and search through all the possible event paths by trellis as much as possible. We use the method of the line difference to compute the distance spectrum of non-causal generating signal systems by defining the line and the line difference to find the distance for every pair of signals. Using this method, we have computed the distance spectrum for non-causal generating signals. Finally, we compare the different spectrums for different non-causal systems of different coefficients.

Abstract High computational complexity constrains truly exhaustive computer searches for good space-time (ST) coded modulations mostly to low constraint length space-time trellis codes (STTrCs). Such codes are primarily devised to achieve maximum transmit diversity gain. Due to their low memory order, optimization based on the design criterion of secondary importance typically results in rather modest coding gains. As another disadvantage of limited freedom, the different low memory order STTrCs are almost exclusively constructed for either slow or fast fading channels. Therefore in practical applications characterized by extremely variable Doppler frequencies, the codes typically fail to demonstrate desired robustness. On the other hand, the main drawback of eventually increased constraint lengths is the prohibitively large decoding complexity, which may increase exponentially if optimal maximum-likelihood decoding (MLD) is applied at the receiver. Therefore, robust ST coded modulation schemes with large equivalent memory orders structured as to allow sub-optimal, low complexity, iterative decoding are needed. To address the aforementioned issues, this thesis proposes parallel concatenated space-time turbo coded modulation (STTuCM). It is among the earliest multiple-input multiple-output (MIMO) coded modulation designs built on the intersection of ST coding and turbo coding. The systematic procedure for building an equivalent recursive STTrC (Rec-STTrC) based on the trellis diagram of an arbitrary non-recursive STTrC is first introduced. The parallel concatenation of punctured constituent Rec-STTrCs designed upon the non-recursive Tarokh et al. STTrCs (Tarokh-STTrCs) is evaluated under different narrow-band frequency flat block fading channels. Combined with novel transceiver designs, the applications for future wide-band code division multiple access (WCDMA) and orthogonal frequency division multiplexing (OFDM) based broadband radio communication systems are considered. The distance spectrum (DS) interpretation of the STTuCM and union bound (UB) performance analysis over slow and fast fading channels reveal the importance of multiplicities in the ST coding design. The modified design criteria for space-time codes (STCs) are introduced that capture the joint effects of error coefficients and multiplicities in the two dimensional DS of a code. Applied to STTuCM, such DS optimization resulted in a new set of constituent codes (CCs) for improved and robust performance over both slow and fast fading channels. A recursive systematic form with a primitive equivalent feedback polynomial is assumed for CCs to assure good convergence in iterative decoding. To justify such assumptions, the iterative decoding convergence analysis based on the Gaussian approximation of the extrinsic information is performed. The DS interpretation, introduced with respect to an arbitrary defined effective Hamming distance (EHD) and effective product distance (EPD), is applicable to the general class of geometrically non-uniform (GNU) CCs. With no constrains on the implemented information interleaving, the STTuCM constructed from newly designed CCs achieves full spatial diversity over quasi-static fading channels, the condition commonly identified as the most restrictive for robust performance over a variety of Doppler spreads. Finally, the impact of bit-wise and symbol-wise information interleaving on the performance of STTuCM is studied.

Efficient multimedia communication over mobile or wireless channels remains a challenging problem. To deal with that problem so far, the industry has followed mostly a divide and conquer approach, by considering separately the source of data (text, image, video, etc.) and the communication channel (electromagnetic waves across the air, a telephone line, a coaxial cable, etc.). The goal is always the same: to transmit (or store) more data reliably per unit of time, of energy, of physical medium, etc. With today's applications, the divide and conquer approach has, in a sense, started to show its limits. Let us consider, for example, the digital transmission of an image. At the transmitter, the first main step is data compression, at the source level. The number of bits that are necessary to represent the image with a given level of quality is reduced, usually by removing details in the image that are invisible (or less visible) to the human eye. The second main step is data protection, at the channel level. The transmission is made ideally resistant to deteriorations caused by the channel, by implementing techniques such as time/frequency/space expansions. In a sense, the two steps are quite antagonistic --- we first compress then expand the original signal --- and have different goals --- compression enables to transfer more data per unit of time/energy/medium while protection enables to transfer data reliably. At the receiver, the "reversed" operations are implemented. This separation in two steps dates back to Shannon's source and channel coding separation theorem in 1948 and has encouraged the division of the research community in two groups, one focusing on data compression, the other on data protection. This separation has also seduced the industry for the design, thereby supported by theory, of layered communication protocols. But this theorem holds only under asymptotic conditions that are rarely satisfied with today's multimedia content and mobile channels. Therefore, it is usually wise in practice to drop this strict separation and to allow at least some cross-layer cooperation between the source and channel layers. This is what lies behind the words joint source-channel techniques. As the name suggests, these techniques are optimized jointly, without a strict separation. Intuitively, since the optimization is less constrained from a mathematical standpoint, the solution can only be better or equivalent. In this thesis, we investigate a promising subset of these techniques, based on the turbo principle and on variable length codes. The potential of this subset has been illustrated for the first time in 2000, with an example that, since then, has been successfully improved in several directions. Unfortunately, most decoding algorithms have been so far developed on an ad hoc basis, without a unified view and often without specifying the approximations made. Besides, most code-related conclusions are based on simulations or on extrinsic information analysis. A theoretical framework on the error correcting properties of variable length codes in turbo systems is lacking. The purpose of this work, in three parts, is to fill in these gaps up to a certain extent. The first part presents the literature in this field and attempts to give a unified overview. The second part proposes a transmission system that generalizes previous systems from the literature, with the simple addition of a repetition code. While most previous systems are designed for bit streams with a high level of residual redundancy, the proposed system has the interesting flexibility to handle easily different levels of redundancy. Its performance is then analyzed for small levels of redundancy, which is a case not tackled extensively in the literature. This analysis leads notably to the discovery of surprising interleaving gains with reversible variable length codes. The third part develops the mathematical framework that was motivated during the second part but skipped on purpose for the sake of clarity. We first clarify several issues that arise with non-uniform bits and the extrinsic information charts, and propose and discuss two methods to compute these charts. Next, several theoretical results are stated on the robustness of variable length codes concatenated with linear error correcting codes. Notably, an approximate average distance spectrum of the concatenated code is rigorously developed. Together with the union bound, this spectrum provides upper bounds on the symbol and frame/packet error rates. These bounds are then analyzed from an interleaving gain standpoint and it is proved that the variable length code improves the interleaving gain if its spectrum is bounded.

Made available in DSpace on 2014-12-17T14:55:43Z (GMT). No. of bitstreams: 1 AlineFGS_DISSERT.pdf: 1151209 bytes, checksum: 4ae192dd7519e3e14977154f7b70d951 (MD5) Previous issue date: 2010-06-14 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / In this work, a performance analysis of transmission schemes employing turbo trellis coded modulation. In general, the performance analysis of such schemes is guided by evaluating the error probability of these schemes. The exact evaluation of this probability is very complex and inefficient from the computational point of view, a widely used alternative is the use of union bound of error probability, because of its easy implementation and computational produce bounds that converge quickly. Since it is the union bound, it should use to expurge some elements of distance spectrum to obtain a tight bound. The main contribution of this work is that the listing proposal is carried out from the puncturing at the level of symbol rather than bit-level as in most works of literature. The main reason for using the symbol level puncturing lies in the fact that the enummerating function of the turbo scheme is obtained directly from complex sequences of signals through the trellis and not indirectly from the binary sequences that require further binary to complex mapping, as proposed by previous works. Thus, algorithms can be applied through matrix from the adjacency matrix, which is obtained by calculating the distances of the complex sequences of the trellis. This work also presents two matrix algorithms for state reduction and the evaluation of the transfer function of this. The results presented in comparisons of the bounds obtained using the proposed technique with some turbo codes of the literature corroborate the proposition of this paper that the expurgated bounds obtained are quite tight and matrix algorithms are easily implemented in any programming software language / Neste trabalho ? feita uma an?lise de desempenho de esquemas de transmiss?o empregando modula??o codificada turbo em treli?a. Em geral, a an?lise de desempenho de tais esquemas ? guiada pelo c?lculo da probabilidade de erro destes esquemas. O c?lculo exato desta probabilidade ? muito complexo e ineficiente sob o ponto de vista computacional, uma alternativa muito utilizada ? o emprego de limitante da uni?o da probabilidade de erro, por ser de f?cil implementa??o computacional e produzir limitantes que convergem rapidamente. Por se tratar do limitante da uni?o, este deve utilizar de expurgo de alguns elementos do espectro de dist?ncias do c?digo para a obten??o de um limitante apertado. A principal contribui??o deste trabalho ? que a enumera??o proposta ? realizada a partir da perfura??o a n?vel de s?mbolo e n?o a n?vel de bit como na maioria dos trabalhos da literatura. O principal motivo do uso da perfura??o a n?vel de s?mbolo reside no fato que a fun??o enumeradora do esquema turbo ? obtida diretamente das seq??ncias complexas de sinais atrav?s da treli?a e n?o de forma indireta a partir da seq??ncias bin?rias que exigem posterior mapeando bin?rio para complexo, como proposto por trabalhos anteriores. Assim, podem ser aplicados algoritmos completamente matriciais a partir da matriz adjac?ncia, que ? obtida a partir do c?lculo das dist?ncias das seq??ncias complexas da treli?a e n?o das seq??ncias bin?rias. Neste trabalho tamb?m s?o apresentados dois algoritmos matriciais de redu??o de estados do codificador bem como do c?lculo da fun??o de transfer?ncia deste. Os resultados apresentados em forma de compara??es dos limitantes obtidos utilizando a t?cnica proposta com alguns c?digos turbo da literatura corroboram com a proposi??o deste trabalho que os limitantes expurgados obtidos s?o apertados e os algoritmos completamente matriciais s?o facilmente implementados em qualquer software de programa??o simb?lica

Avec l’avènement de l’ère intellectuelle et de l’Internet of Everything (IoE), les besoins de la communication mondiale et des applications diverses ont explosé. Cette révolution exige que les futurs réseaux de communication soient plus efficaces, intellectuels, agiles et évolutifs. De nombreuses technologies réseau sont apparues pour répondre à la tendance des réseaux de communication de nouvelle génération tels que les réseaux optiques élastiques (EONs) et la virtualisation de réseau. De nombreux défis apparaissent avec les apparences de la nouvelle architecture et de la nouvelle technologie, telles que le routage et l’allocation de ressource spectrale (RSA) dans les EONs et l’intégration de réseaux virtuels (Virtual Network Embedding ou VNE) dans la virtualisation de réseau.Cette thèse traite la conception et l’analyse d’algorithmes d’approximation dans trois problèmes d’optimation du RSA et du VNE : les impacts de la distribution du trafic et de la topologie du réseau sur le routage tout optique, de l’allocation de ressource spectrale, et du VNE dans les topologies des chemins et cycles. Pour le routage tout optique, le premier sous-problème du RSA, il y a toujours un problème en suspens concernant l’impact de la distribution du trafic et de la topologie EON. Comme le routage tout optique joue un rôle essentiel pour la performance globale de la RSA, cette thèse fournit une analyse approfondi théorique sur ces impacts. Pour le deuxième sous-problème du RSA, l’allocation de ressource spectrale, deux chemins optiques quelconques partageant des fibres optiques communes pourraient devoir être isolés dans le domaine spectral avec une bande de garde appropriée pour empêcher la diaphonie et / ou réduire les menaces de sécurité de la couche physique. Cette thèse considère le scénario dans lequel les exigences de bandes de garde réelles optiques sont différentes pour différentes paires de chemins, et étudie comment affecter les ressources spectrales efficacement dans une telle situation. L’hétérogénéité de la topologie des demandes de réseau virtuel (VNR) est un facteur important qui entrave les performances de la VNE. Cependant, dans de nombreuses applications spécialisées, les VNR ont des caractéristiques structurelles communes par exemple, des chemins et des cycles. Pour obtenir de meilleurs résultats, il est donc essentiel de concevoir des algorithmes dédiés pour ces applications en tenant compte des caractéristiques topologiques. Dans cette thèse, nous prouvons que les problèmes VNE dans les topologies de chemin et de cycle sont NP-difficiles. Afin de les résoudre, nous proposons des algorithmes efficaces également analysons leurs ratios d’approximation / With the coming of intellectual era and Internet of Everything (IoE), the needs of worldwide communication and diverse applications have been explosively growing. This information revolution requires the future communication networks to be more efficient, intellectual, agile and scalable. Many technologies have emerged to meet the requirements of next generation communication networks such as Elastic Optical Networks (EONs) and networking virtualization. However, there are many challenges coming along with them, such as Routing and Spectrum Assignment (RSA) in EONs and Virtual Network Embedding (VNE) in network virtualization. This dissertation addresses the algorithm design and analysis for these challenging problems: the impacts of traffic distribution and network topology on lightpath routing, the distance spectrum assignment and the VNE problem for paths and cycles.For lightpath routing, the first subproblem of the RSA, there is always a pending issue that how the changes of the traffic distribution and EON topology affect it. As the lightpath routing plays a critical role in the overall performance of the RSA, this dissertation provides a thoroughly theoretical analysis on the impacts of the aforementioned two key factors. To this end, we propose two theoretical chains, and derive the optimal routing scheme taking into account two key factors. We then treat the second subproblem of RSA, namely spectrum assignment. Any two lightpaths sharing common fiber links might have to be isolated in the spectrum domain with a proper guard-band to prevent crosstalk and/or reduce physical-layer security threats. We consider the scenario with diverse guard-band sizes, and investigate how to assign the spectrum resources efficiently in such a situation. We provide the upper and lower bounds for the optimal solution of the DSA, and further devise an efficient algorithm which can guarantee approximation ratios in some graph classes.The topology heterogeneity of Virtual Network Requests (VNRs) is one important factor hampering the performance of the VNE. However, in many specialized applications, the VNRs are of some common structural features e.g., paths and cycles. To achieve better outcomes, it is thus critical to design dedicated algorithms for these applications by accounting for topology characteristics. We prove the NP-Harness of path and cycle embeddings. To solve them, we propose some efficient algorithms and analyze their approximation ratios.