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

This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes $A$ and $B$ choose their symbols, $S_A$ and $S_B$, from a small non-binary field, $\mathbb{F}$, and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination ${aS_A+bS_B}$ over $\mathbb{F}$ from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain $S_A$ and $S_B$ explicitly at the relay is overly ambitious when the relay only needs $aS_B+bS_B$. For the binary case, the only possible network-coded combination, ${S_A+S_B}$ over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients $(a,b)$. As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases.

This thesis investigates channel-coded physical layer network coding, in which the relay directly transforms the noisy superimposed channel-coded packets received from the two end nodes, to the network-coded combination of the source packets. This is in contrast to the traditional multiple-access problem, in which the goal is to obtain each message explicitly at the relay. Here, the end nodes $A$ and $B$ choose their symbols, $S_A$ and $S_B$, from a small non-binary field, $\mathbb{F}$, and use non-binary PSK constellation mapper during the transmission phase. The relay then directly decodes the network-coded combination ${aS_A+bS_B}$ over $\mathbb{F}$ from the noisy superimposed channel-coded packets received from two end nodes. Trying to obtain $S_A$ and $S_B$ explicitly at the relay is overly ambitious when the relay only needs $aS_B+bS_B$. For the binary case, the only possible network-coded combination, ${S_A+S_B}$ over the binary field, does not offer the best performance in several channel conditions. The advantage of working over non-binary fields is that it offers the opportunity to decode according to multiple decoding coefficients $(a,b)$. As only one of the network-coded combinations needs to be successfully decoded, a key advantage is then a reduction in error probability by attempting to decode against all choices of decoding coefficients. In this thesis, we compare different constellation mappers and prove that not all of them have distinct performance in terms of frame error rate. Moreover, we derive a lower bound on the frame error rate performance of decoding the network-coded combinations at the relay. Simulation results show that if we adopt concatenated Reed-Solomon and convolutional coding or low density parity check codes at the two end nodes, our non-binary constellations can outperform the binary case significantly in the sense of minimizing the frame error rate and, in particular, the ternary constellation has the best frame error rate performance among all considered cases.

Dans le domaine des réseaux satellitaires, l'apparition de terminaux interactifs à bas-prix nécessite le développement et la mise en œuvre de protocoles d'accès multiple capables de supporter différents profils d'utilisateurs. En particulier, l'Agence Spatiale Européenne (ESA) et le centre d'étude spatial allemand (DLR) ont récemment proposé des protocoles d'accès aléatoires basés sur le codage réseau couche physique et l'élimination itérative des interférences pour résoudre en partie le problème de collisions sur une voie de retour du type Slotted ALOHA. C'est dans ce contexte que s'inscrit cette thèse qui vise à fournir une amélioration dans des méthodes d'accès aléatoires existantes. Nous introduisons Multi-Slot Coded Aloha (MuSCA) comme une nouvelle généralisation of CRDSA. Au lieu de transmettre des copies du même paquet, l'émetteur envoie plusieurs parties d'un mot de code d'un code correcteur d'erreurs ; chaque partie étant précédée d'un entête permettant de localiser les autres parties du mot de code. Au niveau du récepteur, toutes les parties envoyées par le même utilisateur, y compris celles qui sont interférées par d'autres signaux, participent au décodage. Le signal décodé est ensuite soustrait du signal total. Ainsi, l'interférence globale est réduite et les signaux restant ont plus de chances d'être décodés. Plusieurs méthodes d'analyse de performance basées sur des concepts théoriques (calcul de capacité, évolution des densités) et sur des simulations sont proposées. Les résultats obtenus montrent un gain très significatif de débit global comparé aux méthodes d'accès existantes. Ce gain peut encore être augmenté en variant le taux de découpe des mots de code. En modifiant certains de ces concepts, nous proposons également une application du codage réseau couche physique basée sur la superposition de modulations pour l'accès déterministe à la voie retour des communications par satellite. Une amélioration du débit est aussi obtenue par rapport à des stratégies plus classiques de multiplexage temporal. / In the domain of satellite networks, the emergence of low-cost interactive terminals motivates the need to develop and implement multiple access protocols able to support different user profiles. In particular, the European Space Agency (ESA) and the German Aerospace Center (DLR) have recently proposed random access protocols such as Contention Resolution Diversity Coded ALOHA (CRDSA) and Irregular Repetition Slotted ALOHA (IRSA). These methods are based on physical-layer network coding and successive interference cancellation in order to attempt to solve the collisions problem on a return channel of type Slotted ALOHA.This thesis aims to provide improvements of existing random access methods. We introduce Multi-Slot Coded Aloha (MuSCA) as a new generalization of CRDSA. Instead of transmitting copies of the same packet, the transmitter sends several parts of a codeword of an error-correcting code ; each part is preceded by a header allowing to locate the other parts of the codeword. At the receiver side, all parts transmitted by the same user, including those are interfered by other signals, are involved in the decoding. The decoded signal is then subtracted from the total signal. Thus, the overall interference is reduced and the remaining signals are more likely to be decoded. Several methods of performance analysis based on theoretical concepts (capacity computation, density evolution) and simulations are proposed. The results obtained show a significant gain in terms of throughput compared to existing access methods. This gain can be even more increased by varying the codewords stamping rate. Following these concepts, we also propose an application of physical-layer network coding based on the superposition modulation for a deterministic access on a return channel of satellite communications. We observe a gain in terms of throughput compared to more conventional strategies such as the time division multiplexing.

Orientador: Prof. Dr. Murilo Bellezoni Loiola / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia da Informação, 2017.

Network coding has emerged as an attractive alternative to routing because of the through put improvement it provides by reducing the number of channel uses. In a wireless scenario, in addition, further improvement can be obtained through Physical layer Network Coding (PNC), a technique in which nodes are allowed to transmit simultaneously, instead of transmitting in orthogonal slots. In this thesis, the design and analysis of network coding schemes are considered, for wireless two-way relaying, multi-user Multiple Access Relay Channel (MARC) and wireline networks. In a wireless two-way relay channel with PNC, the simultaneous transmissions of user nodes result in Multiple Access Interference (MAI) at there lay node. The harmful effect of MAI is the presence of signal set dependent deep channel fade conditions, called singular fade states, under which the minimum distance of the effective constellation at the relay become zero. Adaptively changing the network coding map used at the relay according to channel conditions greatly reduces the impact of this MAI. In this work, we obtain these adaptive PNC maps, which are finite in number ,by completing partially filled Latin Squares and using graph vertex coloring. Having obtained the network coding maps, the set of all possible channel realizations is quantized into a finite number of regions, with a specific network coding map chosen in a particular region and such a quantization is obtained analytically for 2λ-PSK signal set. The performance of the adaptive PNC scheme for two-way relaying is analyzed and tight high SNR upper bounds are obtained for the average end-to-end symbol error probability, in terms of the average error probability of a point-to-point fading channel. The adaptive PNC scheme is generalized for two-way relaying with multiple antennas at the nodes. As an alternative to the adaptive PNC scheme for two-way relaying, a Distributed Space Time Coding (DSTC) scheme is proposed, which effectively re-moves the effect of singular fade states at the transmitting nodes itself without any Channel State Information at the Transmitter (CSIT), and without any need to change the PNC map as a function of channel fade conditions. It is shown that the singular fade states can be viewed equivalently as vector subspaces of C2, which are referred to as the singular fade subspaces. DSTC design criterion to minimize the number of singular fade subspaces and maximize the coding gain is formulated and explicit low decoding complexity DSTC designs are provided. For the K-user MARC, in which K source nodes want to transmit messages to a destination node D with the help of are lay node R, a new PNC scheme is proposed. Use of a many-to-one PNC map with conventional minimum squared Euclidean distance decoding at D, results in a loss of diversity order due to error propagation from the relay node. To counter this, we propose a novel low complexity decoder which offers the maximum diversity order of two. Next, we consider wire line networks and explore the connections between linear network coding, linear index coding and discrete polymatroids, which are the multi-set analogue of matroids. We define a discrete polymatroidal network and show that a fractional vector linear solution over a field Fq exists for a network if and only if the network is discrete polymatroidal with respect to a discrete polymatroid representable over Fq.An algorithm to construct networks starting from certain class of discrete polymatroids is provided. Every representation over Fq for the discrete polymatroid, results in a fractional vector linear solution over Fq for the constructed network. It is shown that a linear solution to an index coding problem exists if and only if there exists a representable discrete polymatroid satisfying certain conditions which are determined by the index coding problem considered. El Rouayheb et. al. showed that the problem of finding a multi-linear representation for a matroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that matroid. Multi-linear representation of a matroid can be viewed as a special case of representation of an appropriate discrete polymatroid. We generalize the result of El Rouayheb et. al. by showing that the problem of finding a representation for a discrete polymatroid can be reduced to finding a perfect linear index coding solution for an index coding problem obtained from that discrete polymatroid.

Le codage réseau est apparu comme une technique alternative au routage au niveau de la couche réseau permettant d'améliorer le débit et d'optimiser l'utilisation de la capacité du réseau. Récemment, le codage réseau a été appliqué au niveau de la couche physique des réseaux sans-fil pour profiter de la superposition naturelle des signaux effectuée par le lien radio. Le codage réseau peut être vue comme un traitement interne du réseau pour lequel différentes techniques de relayage peuvent être utilisées. Cette thèse étudie un ensemble de traitements ayant des compromis variés en terme de performance et complexité. Nous considérons le canal bidirectionnel à relais, un modèle de canal de communication typique dans les réseaux coopératifs, où deux terminaux s'échangent mutuellement des messages par l'intermédiaire d'un relais. La communication se déroule en deux phases, une phase à accès multiple et une phase de broadcast. Pour ce scénario, nous analysons, dans une première partie, une stratégie de "decode-and-forward". Nous considérons, pour cette étude, des alphabets de taille finie et nous calculons les probabilités moyennes d'erreur de bout-en-bout en se basant sur la métrique d'exposant d'erreur du codage aléatoire. Puis, nous dérivons les régions des débits atteignables par rapport à une probabilité d'erreur maximale tolérable au niveau de chaque nœud. Dans une deuxième partie de la thèse, nous proposons deux schémas de codage réseau pratiques, avec complexité réduite, qui se basent sur la stratégie de relayage "compress-and-forward" (CF). Le premier schéma utilise un codage en réseau de points imbriqués (nested lattices). Le deuxième schéma est une version améliorée qui permet d'atteindre des débits de données supérieurs pour l'utilisateur qui a les meilleures conditions canal. Nous construisons les régions des débits atteignables par les deux schémas proposés tout en optimisant la répartition du temps alloué à chacune des deux phases de transmission. Après l'étude du régime asymptotique, nous analysons le schéma de codage CF avec des réseaux de points de dimension finie. Nous nous concentrons sur le problème de la transmission analogique où la distorsion est optimisée. Enfin, nous étudions l'application d'un schéma de codage, basé sur la stratégie CF avec des réseaux de points imbriqués, pour le canal bidirectionnel à canaux parallèles. Ainsi, nous présentons deux régions de débits atteignables selon la technique de traitement, conjoint ou séparé, des sous-canaux par le relais. / Network coding has emerged as an alternative technique to routing that enhances the throughput at the network layer. Recently, network coding has been applied at the physical layer to take advantage of the natural signal superposition that occurs in the radio link. In this context, the physical-layer network coding can be seen as an in-network processing strategy for which multiple forwarding schemes can be proposed. This thesis investigates a set of processing schemes tailored to the network coding at the physical layer with various compromises between performance and complexity. We consider a two-way relay channel, a typical communication system in cooperative networks, where two terminals communicate with each other via a relay node. This communication occurs during two transmission phases, namely a multiple-access phase and a broadcast phase. For TWRC scenario, we first analyze a decode-and-forward strategy with finite size alphabets. We calculate the end-to-end average error probabilities based on random coding error exponents. Then, we derive the achievable rate regions with respect to a maximal probability of error allowed at each terminal. Next, we propose two low-complexity and practical schemes based on compress-and-forward relaying strategy. The first scheme employs nested lattice coding. The second is an improved version which enables higher data rates for the user experiencing the best channel conditions. We present an information-theoretic framework to reconstruct the achievable rate regions of both schemes by considering optimal time division between both transmission phases. After the asymptotic regime analysis, we study single-layer lattice coding scheme with finite dimension lattices. We focus on the analog transmission problem where the distortion is optimized. Finally, we investigate single-layer lattice coding scheme for parallel Gaussian two-way relay channel. We present two achievable rate regions based on whether the relay processes all the sub-channels jointly or separately.

Abstract The thesis concentrates on evaluating and improving performances of various multiple-input multiple-output (MIMO) relaying scenarios that are particularly relevant to future wireless systems. A greater emphasis is placed on important practical situations, considering relay deployments, availability of channel state information (CSI), limitations of spectrum, and information secrecy. Initially, the performance of a non-coherent amplify-and-forward (AF) MIMO relaying is analyzed when the relay is deployed with the relay-to-destination channel having a line-of-sight (LoS) path. The main attention is given to analyzing the performance of orthogonal space-time block coded based non-coherent AF MIMO system. Exact expressions of statistical parameters and performance metrics are derived considering the instantaneous signal-to-noise ratio (SNR) received at the destination. These performance metrics reveal that a strong LoS component in relay-destination channel always limits the performance promised by MIMO scattering environment when both nodes have multiple antennas. The thesis also considers scenarios in MIMO two-way relaying (TWR) with physical layer network coding (PNC) mapping at the relay. PNC mapping becomes complex with multiple streams being combined at the relay node. Joint precoder-decoder schemes are considered to ease this, and various studies are carried out depending on the CSI. The zero-forcing criterion is used at the nodes when perfect CSI is available. For the imperfect CSI scenario, a robust joint precoder-decoder design is considered. The precoder and decoder matrices are obtained by solving optimization problems, which are formulated to maximize sum-rate and minimize weighted mean square error (WMSE) under transmit power constraints on the nodes. Next, a precoder-decoder scheme for MIMO underlay device-to-device (D2D) communication system is investigated by considering two D2D modes; PNC based D2D and direct D2D. The joint design is based on minimizing mean square error (MSE) which is useful to mitigate interference, and to improve the performance of both D2D and cellular communications. Distributed and centralized algorithms are proposed considering bi-directional communication in both D2D and cellular communications. System performance is discussed with two transmit mode selection schemes as dynamic and static selection schemes. The results show that the PNC based D2D mode extends the coverage area of D2D communication. Finally, secure beamforming schemes for the PNC based MIMO TWR systems are investigated when multiple eavesdroppers are attempting to intercept the user information. The CSI of the user-to-eavesdropper channels is imperfect at the users. The channel estimation errors are assumed with both ellipsoidal bound and Gaussian Markov uncertainty models. Robust optimization problems are formulated considering both scenarios to design beamforming vectors at the users and relay. Numerical results suggest that the proposed algorithms converge fast and provide higher security. / Tiivistelmä Tässä väitöskirjassa keskitytään arvioimaan ja parantamaan suorituskykyä useissa moniantennitoistinjärjestelmissä, jotka ovat ajankohtaisia tulevaisuuden langattomissa verkoissa. Erityisesti työssä analysoidaan tärkeitä käytännön tilanteita, sisältäen toistimien sijoittamisen, kanavatiedon saatavuuden, rajoitetun taajuuskaistan ja tiedon salauksen. Aluksi epäkoherentin, vahvistavan ja jatkolähettävän moniantennitoistimen suorituskykyä analysoidaan tilanteessa, jossa toistin on sijoitettu siten, että kohteeseen on suora yhteys. Suorituskyvyn arvioinnin pääkohteena on ortogonaalinen tila-aika-tason lohkokoodattu epäkoherentti vahvistava ja jatkolähettävä moniantennitoistin. Työssä johdetaan tarkat lausekkeet tilastollisille parametreille ja suorituskykymittareille ottaen huomioon hetkellinen signaalikohinasuhde vastaanottimessa. Nämä suorituskykymittarit ilmaisevat, että toistimen ja kohteen välillä oleva vahva suoran yhteyden komponentti rajoittaa sitä suorituskykyä, jota moniantennijärjestelmän hajontaympäristö ennustaa. Työssä tutkitaan myös kahdensuuntaisia moniantennitoistimia, jotka käyttävät fyysisen kerroksen verkkokoodausta. Koodauksesta tulee monimutkaista, kun monia datavirtoja yhdistetään toistimessa. Tämän helpottamiseksi käytetään yhdistettyä esikoodaus-dekoodausmenetelmää, jota tutkitaan erilaisten kanavatietojen tapauksissa. Täydellisen kanavatiedon tapauksessa käytetään nollaanpakotuskriteeriä. Epätäydellisen kanavatiedon tapauksessa käytetään robustia yhdistettyä esikoodaus-dekoodausmenetelmää. Esikoodaus- ja dekoodausmatriisit saadaan ratkaisemalla optimointiongelmat. Nämä ongelmat on muodostettu maksimoimaan summadatanopeus, ja minimoimaan painotettu keskineliövirhe, kun optimointirajoitteina ovat solmujen lähetystehot. Seuraavaksi esikoodaus-dekoodausmenetelmää tutkitaan moniantennijärjestelmässä, jossa käytetään kahdentyyppistä laitteesta-laitteeseen (D2D) kommunikaatiomenetelmää: fyysisen kerroksen verkkokoodaukseen pohjautuvaa D2D- ja suoraa D2D-kommunikaatiota. Yhteissuunnittelu perustuu keskineliövirheen minimointiin, joka on hyödyllistä, kun halutaan vähentää häiriötä ja parantaa molempien verkkojen suorituskykyä. Työssä ehdotetaan hajautettuja ja keskitettyjä algoritmeja tilanteessa, jossa käytetään kaksisuuntaista kommunikaatiota molemmissa verkoissa. Järjestelmän suorituskykyä arvioidaan, kun käytetään kahta eri lähetystilan valintaa, dynaamista ja staattista. Tulokset osoittavat, että fyysisen kerroksen verkkokoodaukseen pohjautuva D2D kasvattaa D2D-kommunikaatiojärjestelmän kantamaa. Lopuksi, turvallisia keilanmuodostustekniikoita arvioidaan fyysisen kerroksen verkkokoodaukseen pohjautuvassa kahdensuuntaisessa moniantennitoistinjärjestelmässä, kun useat salakuuntelijat yritävät siepata käyttäjätiedon. Käyttäjillä on epäideaalinen kanavatieto heidän ja salakuuntelijoiden välisten linkkien kanavista. Kanavatiedon estimointivirheitä arvioidaan ellipsoidisella ja Gauss-Markov-epävarmuusmallilla. Robustit optimointiongelmat, joissa suunnitellaan keilanmuodostusvektorit käyttäjän ja toistimen välille, muodostetaan molemmille malleille. Numeeriset tulokset osoittavat, että ehdotetut algoritmit konvergoituvat nopeasti ja tarjoavat korkeamman turvallisuuden.