Transmitting quantum information across quantum channels is an important task. However quantum information is delicate, and is easily corrupted. We address the task of protecting quantum information from an information theoretic perspective -- we encode some message qudits into a quantum code, send the encoded quantum information across the noisy quantum channel, then recover the message qudits by decoding. In this dissertation, we discuss the coding problem from several perspectives.} The noisy quantum channel is one of the central aspects of the quantum coding problem, and hence quantifying the noisy quantum channel from the physical model is an important problem. We work with an explicit physical model -- a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling, where the bath oscillator is initially in a thermal-like state. In particular, we treat the completely positive and trace preserving map on the system as a quantum channel, and study the truncation of the channel by truncating its Kraus set. We thereby derive the matrix elements of the Choi-Jamiolkowski operator of the corresponding truncated channel, which are truncated transition amplitudes. Finally, we give a computable approximation for these truncated transition amplitudes with explicit error bounds, and perform a case study of the oscillators in the off-resonant and weakly-coupled regime numerically. In the context of truncated noisy channels, we revisit the notion of approximate error correction of finite dimension codes. We derive a computationally simple lower bound on the worst case entanglement fidelity of a quantum code, when the truncated recovery map of Leung et. al. is rescaled. As an application, we apply our bound to construct a family of multi-error correcting amplitude damping codes that are permutation-invariant. This demonstrates an explicit example where the specific structure of the noisy channel allows code design out of the stabilizer formalism via purely algebraic means. We study lower bounds on the quantum capacity of adversarial channels, where we restrict the selection of quantum codes to the set of concatenated quantum codes. The adversarial channel is a quantum channel where an adversary corrupts a fixed fraction of qudits sent across a quantum channel in the most malicious way possible. The best known rates of communicating over adversarial channels are given by the quantum Gilbert-Varshamov (GV) bound, that is known to be attainable with random quantum codes. We generalize the classical result of Thommesen to the quantum case, thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum GV bound. The outer codes are quantum generalized Reed-Solomon codes, and the inner codes are random independently chosen stabilizer codes, where the rates of the inner and outer codes lie in a specified feasible region. We next study upper bounds on the quantum capacity of some low dimension quantum channels. The quantum capacity of a quantum channel is the maximum rate at which quantum information can be transmitted reliably across it, given arbitrarily many uses of it. While it is known that random quantum codes can be used to attain the quantum capacity, the quantum capacity of many classes of channels is undetermined, even for channels of low input and output dimension. For example, depolarizing channels are important quantum channels, but do not have tight numerical bounds. We obtain upper bounds on the quantum capacity of some unital and non-unital channels -- two-qubit Pauli channels, two-qubit depolarizing channels, two-qubit locally symmetric channels, shifted qubit depolarizing channels, and shifted two-qubit Pauli channels -- using the coherent information of some degradable channels. We use the notion of twirling quantum channels, and Smith and Smolin's method of constructing degradable extensions of quantum channels extensively. The degradable channels we introduce, study and use are two-qubit amplitude damping channels. Exploiting the notion of covariant quantum channels, we give sufficient conditions for the quantum capacity of a degradable channel to be the optimal value of a concave program with linear constraints, and show that our two-qubit degradable amplitude damping channels have this property.

Isopods in the genus Tylos are distributed in tropical and subtropical sandy intertidal beaches throughout the world. These isopods have biological characteristics that are expected to severely restrict their long-distance dispersal potential: (1) they are direct developers (i.e., as all peracarids, they lack a planktonic stage); (2) they cannot survive in the sea for long periods of immersion (i.e., only a few hours); (3) they actively avoid entering the water; and (4) they are restricted to the sandy intertidal portion that is wet, but not covered by water. Because of these traits, high levels of genetic differentiation are anticipated among allopatric populations of Tylos. We studied the phylogeographic patterns of Tylos in the northern East Pacific region between southern California and central Mexico, including the Gulf of California. We discovered high levels of cryptic biodiversity for this isopod, consistent with expectations from its biology. We interpreted the phylogeographic patterns of Tylos in relation to past geological events in the region, and compared them with those of Ligia, a co-distributed non-vagile coastal isopod. Furthermore, we assessed the usefulness of the shape of the ventral plates of the fifth pleonite for distinguishing genetically divergent lineages of Tylos in the study area. Finally, mitochondrial phylogenenetic analyses to identify the most appropriate outgroup taxa for Tylos in the study area, which included 17 of the 21 currently recognized species, provided important insights on the evolutionary history of this genus.

In this thesis, we present low latency general concatenated code structures suitable for parallel processing. We propose parallel decodable serially concatenated codes (PDSCCs) which is a general structure to construct many variants of serially concatenated codes. Using this most general structure we derive parallel decodable serially concatenated convolutional codes (PDSCCCs). Convolutional product codes which are instances of PDSCCCs are studied in detail. PDSCCCs have much less decoding latency and show almost the same performance compared to classical serially concatenated convolutional codes. Using the same idea, we propose parallel decodable turbo codes (PDTCs) which represent a general structure to construct parallel concatenated codes. PDTCs have much less latency compared to classical turbo codes and they both achieve similar performance. We extend the approach proposed for the construction of parallel decodable concatenated codes to trellis coded modulation, turbo channel equalization, and space time trellis codes and show that low latency systems can be constructed using the same idea. Parallel decoding operation introduces new problems in implementation. One such problem is memory collision which occurs when multiple decoder units attempt accessing the same memory device. We propose novel interleaver structures which prevent the memory collision problem while achieving performance close to other interleavers.

In wireless communications, knowledge of the channel coefficients is required for coherent demodulation. In this thesis, a blind channel estimation method based on the Lloyd-Max algorithm is proposed for single-tap fading channels. The algorithm estimates the constellation points for the received signal using an iterative least squares approach. The algorithm is investigated for fast-frequency hopping systems with small block lengths and operating under partial-band and partial-time jamming for both detecting the jammer and estimating the channel. The performance of the Lloyd-Max channel estimation algorithm is compared to the performance of pilot-based channel estimation algorithms which also use the least squares approach and non-coherent demodulation and decoding.

The objective of this thesis is to improve the performance of real-time communication overa wireless channel, by means of specifically tailored channel coding. The deadlinedependent coding (DDC) communication protocol presented here lets the timeliness and thereliability of the delivered information constitute quality of service (QoS) parametersrequested by the application. The values of these QoS parameters are transformed intoactions taken by the link layer protocol in terms of adaptive coding strategies.Incremental redundancy hybrid automatic repeat request (IR-HARQ) schemes usingrate compatible punctured codes are appealing since no repetition of previously transmittedbits is made. Typically, IR-HARQ schemes treat the packet lengths as fixed and maximizethe throughput by optimizing the puncturing pattern, i.e. the order in which the coded bitsare transmitted. In contrast, we define an IR strategy as the maximum number of allowedtransmissions and the number of code bits to include in each transmission. An approach isthen suggested to find the optimal IR strategy that maximizes the average code rate, i.e., theoptimal partitioning of n-kparity bits over at most M transmissions, assuming a givenpuncturing pattern. Concatenated coding used in IR-HARQ schemes provides a new arrayof possibilities for adaptability in terms of decoding complexity and communication timeversus reliability. Hence, critical reliability and timing constraints can be readily evaluatedas a function of available system resources. This in turn enables quantifiable QoS and thusnegotiable QoS. Multiple concatenated single parity check codes are chosen as examplecodes due to their very low decoding complexity. Specific puncturing patterns for thesecomponent codes are obtained using union bounds based on uniform interleavers. Thepuncturing pattern that has the best performance in terms of frame error rate (FER) at a lowsignal-to-noise ratio (SNR) is chosen. Further, using extrinsic information transfer (EXIT)analysis, rate compatible puncturing ratios for the constituent component code are found.The puncturing ratios are chosen to minimize the SNR required for convergence.The applications targeted in this thesis are not necessarily replacement of cables inexisting wired systems. Instead the motivation lies in the new services that wireless real-time communication enables. Hence, communication within and between cooperatingembedded systems is typically the focus. The resulting IR-HARQ-DDC protocol presentedhere is an efficient and fault tolerant link layer protocol foundation using adaptiveconcatenated coding intended specifically for wireless real-time communications. / Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, 2198, Technical report. D, 29,

Transmitting quantum information across quantum channels is an important task. However quantum information is delicate, and is easily corrupted. We address the task of protecting quantum information from an information theoretic perspective -- we encode some message qudits into a quantum code, send the encoded quantum information across the noisy quantum channel, then recover the message qudits by decoding. In this dissertation, we discuss the coding problem from several perspectives.} The noisy quantum channel is one of the central aspects of the quantum coding problem, and hence quantifying the noisy quantum channel from the physical model is an important problem. We work with an explicit physical model -- a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling, where the bath oscillator is initially in a thermal-like state. In particular, we treat the completely positive and trace preserving map on the system as a quantum channel, and study the truncation of the channel by truncating its Kraus set. We thereby derive the matrix elements of the Choi-Jamiolkowski operator of the corresponding truncated channel, which are truncated transition amplitudes. Finally, we give a computable approximation for these truncated transition amplitudes with explicit error bounds, and perform a case study of the oscillators in the off-resonant and weakly-coupled regime numerically. In the context of truncated noisy channels, we revisit the notion of approximate error correction of finite dimension codes. We derive a computationally simple lower bound on the worst case entanglement fidelity of a quantum code, when the truncated recovery map of Leung et. al. is rescaled. As an application, we apply our bound to construct a family of multi-error correcting amplitude damping codes that are permutation-invariant. This demonstrates an explicit example where the specific structure of the noisy channel allows code design out of the stabilizer formalism via purely algebraic means. We study lower bounds on the quantum capacity of adversarial channels, where we restrict the selection of quantum codes to the set of concatenated quantum codes. The adversarial channel is a quantum channel where an adversary corrupts a fixed fraction of qudits sent across a quantum channel in the most malicious way possible. The best known rates of communicating over adversarial channels are given by the quantum Gilbert-Varshamov (GV) bound, that is known to be attainable with random quantum codes. We generalize the classical result of Thommesen to the quantum case, thereby demonstrating the existence of concatenated quantum codes that can asymptotically attain the quantum GV bound. The outer codes are quantum generalized Reed-Solomon codes, and the inner codes are random independently chosen stabilizer codes, where the rates of the inner and outer codes lie in a specified feasible region. We next study upper bounds on the quantum capacity of some low dimension quantum channels. The quantum capacity of a quantum channel is the maximum rate at which quantum information can be transmitted reliably across it, given arbitrarily many uses of it. While it is known that random quantum codes can be used to attain the quantum capacity, the quantum capacity of many classes of channels is undetermined, even for channels of low input and output dimension. For example, depolarizing channels are important quantum channels, but do not have tight numerical bounds. We obtain upper bounds on the quantum capacity of some unital and non-unital channels -- two-qubit Pauli channels, two-qubit depolarizing channels, two-qubit locally symmetric channels, shifted qubit depolarizing channels, and shifted two-qubit Pauli channels -- using the coherent information of some degradable channels. We use the notion of twirling quantum channels, and Smith and Smolin's method of constructing degradable extensions of quantum channels extensively. The degradable channels we introduce, study and use are two-qubit amplitude damping channels. Exploiting the notion of covariant quantum channels, we give sufficient conditions for the quantum capacity of a degradable channel to be the optimal value of a concave program with linear constraints, and show that our two-qubit degradable amplitude damping channels have this property.

Στη σύγχρονη εποχή η ανάγκη για αξιοπιστία των δεδομένων στις νέες τηλεπικοινωνιακές εφαρμογές έχει οδηγήσει στη ανάπτυξη και βελτιστοποίηση των λεγόμενων κωδικών διόρθωσης λαθών. Πρόκειται για συστήματα που έχουν την δυνατότητα ανίχνευσης και διόρθωσης λαθών που εισέρχονται σε τμήμα της πληροφορίας που μεταφέρεται μέσω τηλεπικοινωνιακών κυρίως δικτύων λόγω του θορύβου από το περιβάλλον και πιο συγκεκριμένα από το κανάλι μετάδοσης. Υπάρχουν αρκετές κατηγορίες από τέτοιους κώδικες διόρθωσης ανάλογα της δομής και της φύσης των αλγορίθμων που χρησιμοποιούν. Οι δύο κυριότερες κατηγορίες είναι οι συνελικτικοί κώδικες και οι γραμμικοί μπλοκ κώδικες με τους οποίους θα ασχοληθούμε.Οι δύο κώδικες που θα χρησιμοποιηθούν στα πλαίσια αυτής της εργασίας είναι οι κώδικες LDPC και οι BCH. Ανήκουν και οι δυο στους γραμμικούς μπλοκ κώδικες. Σκοπός της παρούσας διπλωματικής εργασίας αποτελεί αρχικά ο σχεδιασμός και η υλοποίηση ενός παραμετρικού συστήματος κωδικοποίησης και αποκωδικοποίησης για δυαδικούς BCH κώδικες διαφόρων μεγεθών. Εκτός της παραμετροποίησης έμφαση δόθηκε στην χαμηλή πολυπλοκότητα του συστήματος, στον υψηλό ρυθμό επεξεργασίας και στην δυνατότητα χρήσης shortening. Σε δεύτερη φάση πραγματοποιήθηκε σύνδεση μεταξύ, του παραπάνω κώδικα BCH, με έναν έτοιμο κώδικα LDPC και ένα κανάλι λευκού προσθετικού θορύβου (AWGN) που σχεδιάστηκαν στα πλαίσια άλλων διπλωματικών εργασιών με τελικό αποτέλεσμα την μελέτη της συμπεριφοράς του συνολικού συστήματος σε θέματα διόρθωσης λαθών και πιο συγκεκριμένα στην μείωση του φαινομένου του error-floor που παρατηρείται στον LDPC κώδικα. Επιπλέον μελετήθηκε η απαίτηση του συστήματος σε πόρους καθώς και ο ρυθμός επεξεργασίας που επιτυγχάνεται. Οι κύριες παράμετροι του κώδικα BCH που μπορούν να μεταβληθούν είναι το μέγεθος της κωδικής λέξης και η διορθωτική ικανότητα που επιτυγχάνεται. / -

Cette thèse est consacrée à l'amélioration des performances de codage/décodage de systèmes de transmission d'images fixes sur des canaux bruités et réalistes. Nous proposons, à cet effet, le développement de méthodes de transmission d'images optimisées en se focalisant sur les deux couches application et physique des réseaux sans fil. Au niveau de la couche application et afin d'assurer une bonne qualité de service, on utilise des algorithmes de compression efficaces permettant au récepteur de reconstruire l'image avec un maximum de fidélité (JPEG2000 et JPWL). Afin d'assurer une transmission sur des canaux sans fil avec un minimum de TEB à la réception, des techniques de transmission, de codage et de modulation avancées sont utilisées au niveau de la couche physique (système MIMO-OFDM, modulation adaptative, CCE, etc). Dans un premier temps, nous proposons un système de transmission robuste d'images codées JPWL intégrant un schéma de décodage conjoint source-canal basé sur des techniques de décodage à entrées pondérées. On considère, ensuite, l'optimisation d'une chaîne de transmission d'images sur un canal MIMO-OFDM sans fil réaliste. La stratégie de transmission d'images optimisée s'appuie sur des techniques de décodage à entrées pondérées et une approche d'adaptation de lien. Ainsi, le schéma de transmission proposé offre la possibilité de mettre en oeuvre conjointement de l'UEP, de l'UPA, de la modulation adaptative, du codage de source adaptatif et de décodage conjoint pour améliorer la qualité de l'image à la réception. Dans une seconde partie, nous proposons un système robuste de transmission de flux progressifs basé sur le principe de turbo décodage itératif de codes concaténés offrant une stratégie de protection inégale de données. Ainsi, l'originalité de cette étude consiste à proposer des solutions performantes d'optimisation globale d'une chaîne de communication numérique pour améliorer la qualité de transmission. / This work is devoted to improve the coding/ decoding performance of a transmission scheme over noisy and realistic channels. For this purpose, we propose the development of optimized image transmission methods by focusing on both application and physical layers of wireless networks. In order to ensure a better quality of services, efficient compression algorithms (JPEG2000 and JPWL) are used in terms of the application layer enabling the receiver to reconstruct the images with maximum fidelity. Furthermore, to insure a transmission on wireless channels with a minimum BER at reception, some transmission, coding and advanced modulation techniques are used in the physical layer (MIMO-OFDM system, adaptive modulation, FEC, etc). First, we propose a robust transmission system of JPWL encoded images integrating a joint source-channel decoding scheme based on soft input decoding techniques. Next, the optimization of an image transmission scheme on a realistic MIMO-OFDM channel is considered. The optimized image transmission strategy is based on soft input decoding techniques and a link adaptation approach. The proposed transmission scheme offers the possibility of jointly implementing, UEP, UPA, adaptive modulation, adaptive source coding and joint decoding strategies, in order to improve the image visual quality at the reception. Then, we propose a robust transmission system for embedded bit streams based on concatenated block coding mechanism offering an unequal error protection strategy. Thus, the novelty of this study consists in proposing efficient solutions for the global optimization of wireless communication system to improve transmission quality.

A afiliação genérica de Fischerella e Hapalosiphon é problemática devido à instabilidade dos caracteres morfológicos. Os gêneros Fischerella e Hapalosiphon são diferenciados pela presença de tricoma multisseriado e uni ou bisseriado, respectivamente. Porém, geneticamente esses caracteres não se mostraram diacríticos para diferenciar gêneros. Estudos moleculares de linhagens isoladas de ecossistemas brasileiros são escassos para Fischerella e inexistentes para Hapalosiphon. Neste estudo, oito linhagens de cianobactérias, pertencentes à família Hapalosiphonaceae, isoladas de água doce e solos brasileiros foram caracterizadas morfologicamente e geneticamente e analisadas para a produção de substâncias bioativas. As análises morfológicas identificaram cinco morfotípos de Fischerella (CENA19, CENA161, CENA212, CENA213, CENA214) e três de Hapalosiphon (CENA63, CENA71, CENA72). As análises filogenéticas do RNAr 16S usando neighbor-joining (NJ) e máxima verossimilhança (MV) colocaram todas as linhagens isoladas em um agrupamento com alto suporte (reamostragens de 99% NJ e MV) contendo membros da ordem Nostocales. Além disso, as linhagens de Fischerella selecionadas para o estudo agruparam-se em um clado interno com alto valor de reamostragem (100% NJ e 86% MV), com exceção da Fischerella CENA19. A posição dessa estirpe na árvore filogenética indica que necessita de revisão taxonômica. As linhagens de solo Hapalosiphon CENA71 e CENA72 também formaram um clado interno separado (99% NJ e 98% MV), mas a linhagem de água doce CENA63 foi colocada em um clado diferente (com valores de reamostragens de 99% NJ e MV), juntamente com linhagens do gênero Hapalosiphon e Westielopsis prolífica SAG 16.93, oriundas de solo. A comparação das análises filogenéticas individuais de regiões dos genes RNAr 16S, rpoC1, rbcL, tufA, e cpcBA-IGS das três linhagens de Hapalosiphon e de duas linhagens de Fischerella, CENA19 e CENA161, mostrou resultados incongruentes devido as diferentes taxas evolutivas desses genes. No entanto, a análise filogenética concatenada desses genes, mostrou que a Fischerella CENA19 agrupou com as duas linhagens de Hapalosiphon CENA71 e CENA72, com alto valor de reamostragem (100%), enquanto que a Fischerella CENA 161 e a Hapalosiphon CENA63 posicionaram-se cada uma em clados separados. Os resultados indicam que a nomenclatura das linhagens de cianobactérias da família Hapalosiphonaceae necessita de revisão. Os extratos intra e extracelulares das linhagens Fischerella sp. CENA161 e CENA19 e Hapalosiphon sp. CENA71 e CENA72 mostraram efeitos inibitórios no crescimento de bactérias patogênicas. As análises em espectrômetro de massas Q-TOF MS/MS indicaram a putativa presença de aeruginopeptina, cianopeptolina, fischerelina, aeruginosina, oscilapeptilida, microcistinas e ácido tumonóico nos extratos. No extrato intracelular da Fischerella sp. CENA161 identificou-se três ou quatro variantes de microcistinas, LR, LL, FR e/ou M(O)R. Fragmentos dos genes mcyA, mcyB, mcyC, mcyD, mcyE, mcyG e mcyI dessa linhagem foram seqüenciados. Nas duas análises filogenéticas realizadas com sequências de aminoácidos de McyE e sequências concatenadas de McyD, McyE e McyG, as enzimas da microcistina sintetase ficaram agrupadas de acordo com os gêneros de cianobactérias indicando um padrão de evolução / The generic affiliation of Fischerella and Hapalosiphon is problematic due to instability of morphological characters. The Fischerella and Hapalosiphon genera are differentiated by the presence of trichome multisseriate and uni or bisseriate, respectively. However, genetically these characters were not diacritical to distinguish genera. Molecular studies of strains isolated from Brazilian ecosystems are scarce for Fischerella and absent for Hapalosiphon. In this study, eight cyanobacterial strains, belonging to Hapalosiphonaceae family, isolated from Brazilian freshwater and soil were morphologically and genetically characterized and analyzed for bioactive compound productions. The morphological analyses identified five Fischerella (CENA19, CENA161, CENA212, CENA213, CENA214) and three Hapalosiphon (CENA63, CENA71, CENA72) morphotypes. The neighbor-Joining (NJ) and maximum likelihood (ML) phylogenetic analyses of 16S rRNA placed all isolated strains in high supported (99% NJ and ML of bootstrap) cluster containing members of the order Nostocales. Furthermore, the Fischerella strains studied were grouped in an internal clade with high bootstrap value (100% NJ and 86% ML), with exception of Fischerella CENA19. The position of this strain in the phylogenetic tree indicates that it needs taxonomical revision. The soil Hapalosiphon strains CENA71 and CENA72 also formed a separated tight internal clade (99% NJ and 98% ML), but the freshwater strain CENA63 was placed in a different clade (99% NJ and ML of bootstrap value) together with Hapalosiphon strains genera and Westielopsis prolifica SAG 16.93, originated from soil. The comparison of the phylogenetic analyses of individual regions of the genes 16S rRNA, rpoC1, rbcL, tufA, and cpcBA-IGS from the three Hapalosiphon strains and the two Fischerella strains CENA19 and CENA161 showed incongruent results due to different evolutionary rates of these genes. However, the concatenated phylogenetic analysis of these genes, showed that Fischerella CENA19 grouped with the two Hapalosiphon strains CENA71 and CENA72 with high bootstrap value (100%), while Fischerella CENA 161 and Hapalosiphon CENA63 were positionated each one in separate clades. The results indicate that the nomenclature of cyanobacterial strains from the family Hapalosiphonaceae needs revision. The intra and extracellular extracts of the Fischerella sp. strains CENA161 and CENA19 and Hapalosiphon sp. strains CENA71 and CENA72 showed inhibitory effects on the growth of pathogenic bacteria. The analysis in the mass spectrometer Q-TOF MS/MS indicated the presence of aeruginopeptin, cyanopeptolin, fischerellin, aeruginosin, oscillapeptilide, microcystins and tumonoic acid in the extracts. In the intracellular extracts of Fischerella sp. CENA161, three or four variants of microcystins, LR, LL, FR and/or M(O)R, were identified. Fragments of genes mcyA, mcyB, mcyC, mcyD, mcyE, mcyG and mcyI of this strain were sequenced. In both phylogenetic analyses performed with amino acid sequences of McyE and concatenated sequences of McyD, McyE and McyG, the microcystin synthetase enzymes were grouped according to the cyanobacterial genera, indicating a pattern of evolution

No description available.