Ο υπολογισμός της χωρητικότητας Shannon ενός τηλεπικοινωνιακού καναλιού είναι ένα από τα κλασικά προβλήματα της θεωρίας πληροφορίας. Η τιμή της προσδιορίζει το μέγιστο δυνατό ρυθμό αξιόπιστης μετάδοσης μέσα από το κανάλι και αποτελεί ρυθμιστική παράμετρο κατά το σχεδιασμό κάθε τηλεπικοινωνιακού συστήματος. Στις πιο ενδιαφέρουσες περιπτώσεις ο υπολογισμός καταλήγει σε ένα πρόβλημα βελτιστοποίησης για το οποίο δε μπορεί να δοθεί αναλυτική λύση, οπότε καταφεύγουμε στη χρήση προσεγγιστικών μεθόδων ή στη διατύπωση φραγμάτων. Στα πλαίσια της εργασίας μελετάται η χωρητικότητα Shannon τηλεπικοινωνιακών καναλιών ενός ή πολλαπλών χρηστών. Η μελέτη ξεκινά από την απλές περιπτώσεις του διακριτού καναλιού χωρίς μνήμη (DMC) και του καναλιού AWGN και επεκτείνεται στις πιο ενδιαφέρουσες περιπτώσεις των σύμφωνων ή μη (coherence/non-coherence) καναλιών διάλειψης, σε κανάλια με μνήμη, κανάλια πολλαπλών κεραιών και κανάλια πολλαπλών χρηστών. Σε κάθε περίπτωση καταγράφονται τα σημαντικότερα ερευνητικά αποτελέσματα σχετικά με το πρόβλημα προσδιορισμού της χωρητικότητας, τη συμπεριφορά της σε σχέση με τους παράγοντες του τηλεπικοινωνιακού μοντέλου, του αλγοριθμικού υπολογισμού της και τα χαρακτηριστικά που πρέπει να έχει η είσοδος ώστε να επιτυγχάνεται η τιμή της. / Computing the Shannon Capacity of a communication channel is one of the classic problems of information theory. Its value determine the maximum possible rate of reliable transmission through the channel and constitutes a design parameter during the designing of the communication system. In most interesting cases the problem ending to an optimization problem which can’t be solved analytically, so we refuge to approximating methods and we can only state bounds for the region in which capacity belongs. In this thesis we study the Shannon Capacity of single user and multiple user communications systems. The study begins with the simple cases of Discrete Memoryless Channel (DMC) and AWGN channel and goes further to more interesting cases like coherence/non-coherence fading channels, channels with memory, multiple antenna channels and channels with multiple users. In each case, we present the most important scientific results considering the problem of capacity, its behavior in relation to the parameters of the communication model, its algorithmic computation and the characteristics of the optimal input.

Los canales múltiple-entrada-múltiple-salida (MIMO) han sido ampliamente propuestos para superar los desvanecimientos aleatorios de canal en comunicaciones inalámbricas no selectivas en frecuencia. Basados en equipar tanto transmisores como receptores con múltiple antenas, sus ventajas son dobles. Por un lado, permiten al transmisor: i) concentrar la energía transmitida en una dirección-propia determinada, o ii) codificar entre antenas con el fin de superar desvanecimientos no conocidos de canal. Por otro lado, facilitan al receptor el muestreo de la señal en el dominio espacial. Esta operación, seguida por la combinación coherente de muestras, aumenta la relación señal a ruido de entrada al receptor. De esta forma, el procesado multi-antena es capaz de incrementar la capacidad (y la fiabilidad) de la transmisión en escenarios con alta dispersión.Desafortunadamente, no siempre es posible emplazar múltiples antenas en los dispositivos inalámbricos, debido a limitaciones de espacio y/o coste. Para estos casos, la manera más apropiada de explotar el procesado multi-antena es mediante retransmisión, consistente en disponer un conjunto de repetidores inalámbricos que asistan la comunicación entre un grupo de transmisores y un grupo de receptores, todos con una única antena. Con la ayuda de los repetidores, por tanto, los canales MIMO se pueden imitar de manera distribuida. Sin embargo, la capacidad exacta de las comunicaciones con repetidores (así como la manera en que este esquema funciona con respeto al MIMO equivalente) es todavía un problema no resuelto. A dicho problema dedicamos esta tesis.En particular, la presente disertación tiene como objetivo estudiar la capacidad de canales Gaussianos asistidos por múltiples repetidores paralelos. Dos repetidores se dicen paralelos si no existe conexión directa entre ellos, si bien ambos tienen conexión directa con la fuente y el destino de la comunicación. Nos centramos en el análisis de tres canales ampliamente conocidos: el canal punto-a-punto, el canal de múltiple-acceso y el canal de broadcast, y estudiamos su mejora de funcionamiento con repetidores. A lo largo de la tesis, se tomarán las siguientes hipótesis: i) operación full-duplex en los repetidores, ii) conocimiento de canal tanto en transmisión como en recepción, y iii) desvanecimiento sin memoria, e invariante en el tiempo.En primer lugar, analizamos el canal con múltiples repetidores paralelos, en el cual una única fuente se comunica con un único destino en presencia de N repetidores paralelos. Derivamos límites inferiores de la capacidad del canal por medio de las tasas de transmisión conseguibles con distintos protocolos: decodificar-y-enviar, decodificar-parcialmente-y-enviar, comprimir-y-enviar, y repetición lineal. Asimismo, con un fin comparativo, proveemos un límite superior, obtenido a través del Teorema de max-flow-min-cut. Finalmente, para el número de repetidores tendiendo a infinito, presentamos las leyes de crecimiento de todas las tasas de transmisión, así como la del límite superior.A continuación, la tesis se centra en el canal de múltiple-acceso (MAC) con múltiples repetidores paralelos. El canal consiste en múltiples usuarios comunicándose simultáneamente con un único destino en presencia de N repetidores paralelos. Derivamos una cota superior de la región de capacidad de dicho canal utilizando, de nuevo, el Teorema de max-flow-min-cut, y encontramos regiones de tasas de transmisión conseguibles mediante: decodificar-y-enviar, comprimir-y-enviar, y repetición lineal. Asimismo, se analiza el valor asintótico de dichas tasas de transmisión conseguibles, asumiendo el número de usuarios creciendo sin límite. Dicho estudio nos permite intuir el impacto de la diversidad multiusuario en redes de acceso con repetidores.Finalmente, la disertación considera el canal de broadcast (BC) con múltiples repetidores paralelos. En él, una única fuente se comunica con múltiples destinos en presencia de N repetidores paralelos. Para dicho canal, derivamos tasas de transmisión conseguibles dado: i) codificación de canal tipo dirty paper en la fuente, ii) decodificar-y-enviar, comprimir-y-enviar, y repetición lineal, respectivamente, en los repetidores. Además, para repetición lineal, demostramos que la dualidad MAC-BC se cumple. Es decir, la región de tasas de transmisión conseguibles en el BC es igual a aquélla del MAC con una limitación de potencia suma. Utilizando este resultado, se derivan algoritmos de asignación óptima de recursos basados en teoría de optimización convexa. / Multiple-input-multiple-output (MIMO) channels are extensively proposed as a means to overcome the random channel impairments of frequency-flat wireless communications. Based upon placing multiple antennas at both the transmitter and receiver sides of the communication, their virtues are twofold. On the one hand, they allow the transmitter: i) to concentrate the transmitted power onto a desired eigen-direction, or ii) tocode across antennas to overcome unknown channel fading. On the other hand, they permit the receiver to sample the signal on the space domain. This operation, followed by the coherent combination of samples, increases the signal-to-noise ratio at the input of the detector. In fine, MIMO processing is able to provide large capacity (and reliability) gains within rich-scattered scenarios.Nevertheless, equipping wireless handsets with multiple antennas is not always possible or worthwhile. Mainly, due to size and cost constraints, respectively. For these cases, the most appropriate manner to exploit multi-antenna processing is by means of relaying. This consists of a set of wireless relay nodes assisting the communication between a set of single-antenna sources and a set of single-antenna destinations. With the aid of relays, indeed, MIMO channels can be mimicked in a distributed way. However, the exact channel capacity of single-antenna communications with relays (and how this scheme performs with respect to the equivalent MIMO channel) is a long-standing open problem. To it we have devoted this thesis.In particular, the present dissertation aims at studying the capacity of Gaussian channels when assisted by multiple, parallel, relays. Two relays are said to be parallel if there is no direct link between them, while both have direct link from the source and towards the destination. We focus on three well-known channels: the point-to-point channel, the multi-access channel and the broadcast channel, and study their performance improvement with relays. All over the dissertation, the following assumptions are taken: i) full-duplex operation at the relays, ii) transmit and receive channel state information available at all network nodes, and iii) time-invariant, memory-less fading.Firstly, we analyze the multiple-parallel relay channel, where a single source communicates to a single destination in the presence of N parallel relays. The capacity of the channel is lower bounded by means of the achievable rates with different relaying protocols, i.e. decode-and-forward, partial decode-and-forward, compress-and-forward and linear relaying. Likewise, a capacity upper bound is provided for comparison, derived using the max-flow-min-cut Theorem. Finally, for number of relays growing to infinity, the scaling laws of all achievable rates are presented, as well as the one of the upper bound.Next, the dissertation focusses on the multi-access channel (MAC) with multiple-parallel relays. The channel consists of multiple users simultaneously communicating to a single destination in the presence of N parallel relay nodes. We bound the capacity region of the channel using, again, the max-flow-min-cut Theorem and find achievable rate regions by means of decode-and-forward, linear relaying and compress-and-forward. In addition, we analyze the asymptotic performance of the obtained achievable sum-rates, given the number of users growing without bound. Such a study allows us to grasp the impact of multi-user diversity on access networks with relays.Finally, the dissertation considers the broadcast channel (BC) with multiple parallel relays. This consists of a single source communicating to multiple receivers in the presence of N parallel relays. For the channel, we derive achievable rate regions considering: i) dirty paper encoding at the source, and ii) decode-and-forward, linear relaying and compress-and-forward, respectively, at the relays. Moreover, for linear relaying, we prove that MAC-BC duality holds. That is, the achievable rate region of the BC is equal to that of the MAC with a sum-power constraint. Using this result, the computation of the channel's weighted sum-rate with linear relaying is notably simplified. Likewise, convex resource allocation algorithms can be derived.

The demand for wireless data services has been dramatically growing over the last decade. This growth has been accompanied by a significant increase in the number of users sharing the same wireless medium, and as a result, interference management has become a hot topic of research in recent years. In this dissertation, we investigate feedback and transmitter cooperation as two closely related tools to manage the interference and achieve high data rates in several wireless networks, focusing on additive white Gaussian noise (AWGN) interference, X, and broadcast channels. We start by a one-to-many network, namely, the three-user multiple-input multiple-output (MIMO) Gaussian broadcast channel, where we assume that the transmitter obtains the channel state information (CSI) through feedback links after a finite delay. We also assume that the feedback delay is greater than the channel coherence time, and thus, the CSI expires prior to being exploited by the transmitter for its current transmission. Nevertheless, we show that this delayed CSI at the transmitter (delayed CSIT) can help the transmitter to achieve significantly higher data rates compared to having no CSI. We indeed show that delayed CSIT increases the channel degrees of freedom (DoF), which is translated to an unbounded increase in capacity with increasing signal-to-noise-ratio (SNR). For the symmetric case, i.e. with the same number of antennas at each receiver, we propose different transmission schemes whose achievable DoFs meet the upper bound for a wide range of transmit-receive antenna ratios. Also, for the general non-symmetric case, we propose transmission schemes that characterize the DoF region for certain classes of antenna configurations. Subsequently, we investigate channels with distributed transmitters, namely, Gaussian single-input single-output (SISO) K-user interference channel and 2×K X channel under the delayed CSIT assumption. In these channels, in major contrast to the broadcast channel, each transmitter has access only to its own messages. We propose novel multiphase transmission schemes wherein the transmitters collaboratively align the past interference at appropriate receivers using the knowledge of past CSI. Our achievable DoFs are greater than one (which is the channel DoF without CSIT), and strictly increasing in K. Our results are yet the best available reported DoFs for these channels with delayed CSIT. Furthermore, we consider the K-user r-cyclic interference channel, where each transmitter causes interference on only r receivers in a cyclic manner. By developing a new upper bound, we show that this channel has K/r DoF with no CSIT. Moreover, by generalizing our multiphase transmission ideas, we show that, for r=3, this channel can achieve strictly greater than K/3 DoF with delayed CSIT. Next, we add the capability of simultaneous transmission and reception, i.e. full-duplex operation, to the transmitters, and investigate its impact on the DoF of the SISO Gaussian K-user interference and M×K X channel under the delayed CSIT assumption. By proposing new cooperation/alignment techniques, we show that the full-duplex transmitter cooperation can potentially yield DoF gains in both channels with delayed CSIT. This is in sharp contrast to the previous results on these channels indicating the inability of full-duplex transmitter cooperation to increase the channel DoF with either perfect instantaneous CSIT or no CSIT. With the recent technological advances in implementation of full-duplex communication, it is expected to play a crucial role in the future wireless systems. Finally, we consider the Gaussian K-user interference and K×K X channel with output feedback, wherein each transmitter causally accesses the output of its paired receiver. First, using the output feedback and under no CSIT assumption, we show that both channels can achieve DoF values greater than one, strictly increasing in K, and approaching the limiting value of 2 as K→∞. Then, we develop transmission schemes for the same channels with both output feedback and delayed CSIT, known as Shannon feedback. Our achievable DoFs with Shannon feedback are greater than those with the output feedback for almost all values of K.

abstract: There are many wireless communication and networking applications that require high transmission rates and reliability with only limited resources in terms of bandwidth, power, hardware complexity etc.. Real-time video streaming, gaming and social networking are a few such examples. Over the years many problems have been addressed towards the goal of enabling such applications; however, significant challenges still remain, particularly, in the context of multi-user communications. With the motivation of addressing some of these challenges, the main focus of this dissertation is the design and analysis of capacity approaching coding schemes for several (wireless) multi-user communication scenarios. Specifically, three main themes are studied: superposition coding over broadcast channels, practical coding for binary-input binary-output broadcast channels, and signalling schemes for two-way relay channels. As the first contribution, we propose an analytical tool that allows for reliable comparison of different practical codes and decoding strategies over degraded broadcast channels, even for very low error rates for which simulations are impractical. The second contribution deals with binary-input binary-output degraded broadcast channels, for which an optimal encoding scheme that achieves the capacity boundary is found, and a practical coding scheme is given by concatenation of an outer low density parity check code and an inner (non-linear) mapper that induces desired distribution of "one" in a codeword. The third contribution considers two-way relay channels where the information exchange between two nodes takes place in two transmission phases using a coding scheme called physical-layer network coding. At the relay, a near optimal decoding strategy is derived using a list decoding algorithm, and an approximation is obtained by a joint decoding approach. For the latter scheme, an analytical approximation of the word error rate based on a union bounding technique is computed under the assumption that linear codes are employed at the two nodes exchanging data. Further, when the wireless channel is frequency selective, two decoding strategies at the relay are developed, namely, a near optimal decoding scheme implemented using list decoding, and a reduced complexity detection/decoding scheme utilizing a linear minimum mean squared error based detector followed by a network coded sequence decoder. / Dissertation/Thesis / Ph.D. Electrical Engineering 2011

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A Broadcast Channel is a communication path between a single source and two or more receivers or users. The source intends to communicate independent information to the users. A particular case of interest is the Gaussian Broadcast Channel (GBC) where the noise at each user is additive white Gaussian noise (AWGN). The capacity region of GBC is well known and the input to the channel is distributed as Gaussian. The capacity region of another special case of GBC namely Fading Broadcast Channel (FBC)was given in [Li and Goldsmith, 2001]and was shown that superposition of Gaussian codes is optimal for the FBC (treated as a vector degraded Broadcast Channel). The capacity region obtained when the input to the channel is distributed uniformly over a finite alphabet(Constellation)is termed as Constellation Constrained(CC) capacity region [Biglieri 2005]. In this thesis the CC capacity region for two-user GBC and the FBC are obtained. In case of GBC the idea of superposition coding with input from finite alphabet and CC capacity was explored in [Hupert and Bossert, 2007]but with some limitations. When the participating individual signal sets are nearly equal i.e., given total average power constraint P the rate reward α (also the power sharing parameter) is approximately equal to 0.5, we show via simulation that with rotation of one of the signal sets by an appropriate angle the CC capacity region is maximally enlarged. We analytically derive the expression for optimal angle of rotation. In case of FBC a heuristic power allocation procedure called finite-constellation power allocation procedure is provided through which it is shown (via simulation)that the ergodic CC capacity region thus obtained completely subsumes the ergodic CC capacity region obtained by allocating power using the procedure given in[Li and Goldsmith, 2001].It is shown through simulations that rotating one of the signal sets by an optimal angle (obtained by trial and error method)for a given α maximally enlarges the ergodic CC capacity region when finite-constellation power allocation is used. An expression for determining the optimal angle of rotation for the given fading state, is obtained. And the effect of rotation is maximum around the region corresponding to α =0.5. For both GBC and FBC superposition coding is done at the transmitter and successive decoding is carried out at the receivers.

Cette thèse explore, sous certains paramètres réalistes, l’une des techniques clés pour les réseaux sans fil de demain, i.e., la réduction des interférences permis par la voie de retour (feedback). Nous nous concentrons sur la voie de retour du type d’état, également connu sous le nom de CSIT retardé, qui aide les récepteurs à profiter des observations indésirables par créer des dimensions de signaux supplémentaires. Afin de vérifier l’utilité de la CSIT retardé dans des situations sévères, nous l’étudions avec SNR fini et / ou avec la hétérogénéité de la voie de retour dans une configuration de communication de diffusion, qui est largement utilisé pour modéliser la transmission de liaison descendante dans les systèmes cellulaires. Tout au long de la thèse, nous utilisons des outils de théorie information, par exemple, le codage lossy distribué, bloc Markov codage, la technique de compression (Wyner-Ziv), etc.Dans la première partie de cette thèse, nous sommes surtout intéressés par la performance de CSIT retardée avec SNR fini et l’uniformité à travers les résultats dans le canal Gaussien et dans le canal d’effacement. Plusieurs schémas relativement simples sont proposés pour des canaux de diffusion multiutilisateur (sans mémoire) dans le cas où les états sont supposés être entièrement connus à la destination, mais causalement à l’émetteur. Lors de l’analyse des régions correspondantes les cas Gaussien/ d’effacement, nous avons caractérisé des améliorations en termes de débits symétriques plus élevés et plus d’options de l’alphabet d’entré.Dans la deuxième partie de cette thèse, les algorithmes adaptés aux hétérogénéités différentes de la voie de retour sont ciblés, c’est-à-dire, seulement une partie des nœuds de communication sont impliqués dans le processus de feedback. En particulier, nous nous concentrons sur le canal de 1) diffusion supporté par les voies de retour des récepteurs partiels, 2) diffusion avec relais et voie de retour au relais. Étant donné que (tous /partiel) états retardés sont accessibles à des émetteurs (tous/partiels), les approches proposées, bien qu’ils emploient les méthodes de codages visant à réduire les interférences à tous les récepteurs, doivent soit donner la priorité aux utilisateurs qui fournissent les états et compter sur un gain de codage opportuniste pour les autres, soit forcer chaque source à prendre la responsabilité partielle de transmission. Les améliorations sur les débits réalisables sont justifiées dans des cas avec analyse et quelques exemples. Les résultats et les évaluations de cette thèse, qui donnent quelques indications sur comment le retour d’état peut être exploité dans la transmission de liaison descendante, montrent qu’une bonne performance de débit pourrait être atteinte avec le CSIT retardé même lorsque la puissance de transmission est limitée et lorsque le retour d’état est disponible de façon hétérogène. / This dissertation explores one of the key techniques for future wireless networks, namely feedback enabled interference mitigation, under some realistic settings. We focus on the state-type feedback, also known as delayed CSIT, which helps leverage receivers’ overheard observations to create extra signal dimensions. In order to verify the usefulness of delayed CSIT in harsh situations, we investigate it with finite SNR and/or feedback heterogeneity in a broadcast communication setup, which is widely utilized to model downlink transmission in cellular systems. Throughout the thesis, we use some information theoretical tools, e.g., distributed lossy source coding, block Markov coding, Wyner-Ziv compression technique, e.t.c.In the first part of this dissertation, we are mainly interested in the finite SNR performance of delayed CSIT and the uniformity across the results in the Gaussian broadcast channel and in the erasure channel. Several relatively simple schemes are proposed in multi-user memoryless broadcast channels when states are assumed to be fully known at the destinations but only strictly causally at the transmitter. Enhancements in terms of higher symmetric rates and more input alphabet options are then characterized when analyzing the corresponding regions in Gaussian/erasure cases.In the second part of this dissertation, algorithms adapted to distinct feedback heterogeneities are targeted as only part of the communication nodes are involved in the feedback process. In particular, we concentrate on 1) broadcast channel with feedback from part of all receivers; and 2) broadcast relay channel with feedback at the relay. Given that (partial) delayed states are accessible at (partial) transmitters, the proposed approaches, though employ coding methods aiming at mitigating interference at all receivers, have to either give priority to the users who feedback and rely on opportunistic coding gain for the others or force each source to take limited responsibility in the transmission. Improvements on achievable rates are justified in either cases with analysis and some examples.The results and their evaluations in this thesis, which give some insights on how to exploit the state feedback in downlink transmission, show that good rate performance can be achieved with delayed CSIT even when transmission power is limited and when the state feedback is heterogeneous.

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No description available.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.