Wireless networks have potential applications in wireless Internet connectivity, battlefields, disaster relief, and cyber-physical systems. While the nodes in these networks communicate with each other over the air, the challenges faced by and the subsequent design criteria of these networks are diverse. In this thesis, we study and discuss a few design requirements of these networks, such as efficient utilization of the network bandwidth in IEEE 802.11 infrastructure networks, evaluating utility of sensor node deployments, and security from eavesdroppers. The presence of infrastructure IEEE 802.11 based Wireless Local Area Networks (WLANs) allows mobile users to seamlessly transfer huge volumes of data. While these networks accommodate mobility, and are a cost-effective alternative to cellular networks, they are well known to display several performance anomalies. We study a few such anomalies, and provide a performance management solution for IEEE 802.11 based WLANs. On the other hand, in sensor networks, the absence of infrastructure mandates the use of adhoc network architectures. In these architectures, nodes are required to route data to gateway nodes over a multi-hop network. These gateway nodes are larger in size, and costlier in comparison with the regular nodes. In this context, we propose a unified framework that can be used to compare different deployment scenarios, and provide a means to design efficient large-scale adhoc networks. In modern times, security has become an additional design criterion in wireless networks. Traditionally, secure transmissions were enabled using cryptographic schemes. However, in recent years, researchers have explored physical layer security as an alternative to these traditional cryptographic schemes. Physical layer security enables secure transmissions at non-zero data rate between two communicating nodes, by exploiting the degraded nature of the eavesdropper channel and the inherent randomness of the wireless medium. Also, in many practical scenarios, several nodes cooperate to improve their individual secrecy rates. Therefore, in this thesis, we also study scenarios, where cooperative schemes can improve secure end-to-end data transmission rates, while adhering to an overall power budget. In spite of the presence of voluminous reservoirs of information such as digital libraries and the Internet, asking around still remains a popular means of seeking information. In scenarios where the person is interested in communal, or location-specific information, such kind of retrieval may yield better results than a global search. Hence, wireless networks should be designed, analyzed and controlled by taking into account the evolution of the underlying social networks. This alliance between social network analysis and adhoc network architectures can greatly advance the design of network protocols, especially in environments with opportunistic communications. Therefore, in addition to the above mentioned problem, in this thesis, we have also presented and studied a model that captures the temporal evolution of information in social networks with memory.

Multiple users compete for a common resource like bandwidth to communicate data in interference networks. Existing approaches in dealing with interference limit the rate of communication due to paucity of shared resources. This limitation in the rate gets more glaring as the number of users in the network increases. For example, existing wireless systems either choose to orthogonalize the users (for example, Frequency Division Multiple Access (FDMA) systems or Code Division Multiple Access (CDMA) systems) or treat interference as Gaussian noise at the receivers. It is well known that these approaches are sub-optimal in general. Orthogonalization of users limit the number of available interference-free channels (known as degrees of freedom, abbreviated as DoF) and treating interference as noise means that the receiver cannot make use of the structure in the interfering signals. This motivates the need to analyze alternate transmit and decoding schemes in interference networks. This thesis mainly analyzes transmit schemes that use linear precoding for various configurations of interference networks with some practical constraints imposed by the use of finite input constellations, propagation delays, and channel state availability at the transmitters. The main contributions of this thesis are listed below. Achievable rates using precoding with finite constellation inputs in Gaussian Interference Channels (GIC) is analyzed. A metric for finding the approximate angle of rotation to maximally enlarge the Constellation Constrained (CC) capacity of two-user Gaussian Strong Interference Channel (GSIC) is proposed. Even as the Gaussian alphabet FDMA rate curve touches the capacity curve of the GSIC, with both the users using the same finite constellation, we show that the CC FDMA rate curve lies strictly inside the CC capacity curve at high powers. For a K-user MIMO GIC, a set of necessary and sufficient conditions on the precoders under which the mutual information between between relevant transmit-receive pairs saturate like in the single user case is derived. Gradient-ascent based algorithms to optimize the sum-rate achieved by precoding with finite constellation inputs and treating interference as noise are proposed. For a class of Gaussian interference networks with general message demands, identified as symmetrically connected interference networks, the expected sumspectral efficiency (in bits/sec/Hz) is shown to grow linearly with the number of transmitters at finite SNR, using a time-domain Interference Alignment (IA) scheme in the presence of line of sight (LOS) channels. For a 2×2 MIMO X-Network with M antennas at each node, we identify spacetime block codes that could be coupled with an appropriate precoding scheme to achieve the maximum possible sum-DoF of 4M 3 , for M = 3, 4. The proposed schemes are shown to achieve a diversity gain of M with SNR-independent finite constellation inputs. The proposed schemes have lower CSIT requirements compared to existing schemes. This thesis also makes an attempt to guarantee a minimum throughput when the zero-interference conditions cannot be satisfied in a wireline network with three unicast sessions with delays, using Precoding Based Network Alignment (PBNA). Three different PBNA schemes namely PBNA with time-varying local encoding coefficients (LECs), PBNA using transform approach and time-invariant LECs, and PBNA using transform approach and block time-varying LECs are proposed and their feasibility conditions analyzed.

Ce manuscrit traite de la fiabilisation des CPL-BE dans le contexte smart grid avec l’application des techniques de codage correcteur d’erreurs et d’effacements. Après une introduction sur le concept de smart grid, le canal CPL-BE est caractérisé précisément et les modèles qui le décrivent sont présentés. Les performances des codes à métrique rang, simples ou concaténés avec des codes convolutifs, particulièrement intéressants pour combattre le bruit criss-cross sur les réseaux CPL-BE sont simulées et comparées aux performances des codes Reed-Solomon déjà présents dans plusieurs standards. Les codes fontaines qui s’adaptent à n’importe quelles statistiques d’effacements sur le canal CPL sont utilisés et les performances de schémas coopératifs basés sur ces codes fontaines sur des réseaux linéaires multi-sauts sont étudiés. Enfin des algorithmes permettant de combiner le codage réseau et le codage fontaine pour la topologie particulière des réseaux CPL pour les smart grid sont proposés et évalués. / This PhD dissertation deals with the mitigation of the impact of the Narrowband PowerLine communication (NB-PLC) channel impairments e.g., periodic impulsive noise and narrowband noise, by applying the error/erasure correction coding techniques. After an introduction to the concept of smart grid, the NB-PLC channels are characterized precisely and models that describe these channels are presented. The performance of rank metric codes, simple or concatenated with convolutional codes, that are particularly interesting to combat criss-cross errors on the NB-PLC networks are simulated and compared with Reed- Solomon (already present in several NB-PLC standards) codes performance. Fountain codes that can adapt to any channel erasures statistics are used for the NB-PLC networks and the performance of cooperative schemes based on these fountain codes on linear multi-hop networks are studied. Finally, algorithms to combine the network coding and fountain codes for the particular topology of PLC networks for the smart grid are proposed and evaluated.

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.

In this thesis, we investigate physical-layer network coding in an L × M × K relay network, where L source nodes want to transmit messages to K sink nodes via M relay nodes. We focus on the information processing at the relay nodes and the compute-and-forward framework. Nested lattice codes are used, which have the property that every linear combination of codewords is a valid codeword. This property is essential for physical-layer network coding. Because the actual network coding occurs on the physical layer, the network coding coefficients are determined by the channel realizations. Finding the optimal network coding coefficients for given channel realizations is a non-trivial optimization problem. In this thesis, we provide an algorithm to find network coding coefficients that result in the highest data rate at a chosen relay. The solution of this optimization problem is only locally optimal, i.e., it is optimal for a particular relay. If we consider a multi-hop network, each potential receiver must get enough linear independent combinations to be able to decode the individual messages. If this is not the case, outage occurs, which results in data loss. In this thesis, we propose a new strategy for choosing the network coding coefficients locally at the relays without solving the optimization problem globally. We thereby reduce the solution space for the relays such that linear independence between their decoded linear combinations is guaranteed. Further, we discuss the influence of spatial correlation on the optimization problem. Having solved the optimization problem, we combine physical-layer network coding with physical-layer secrecy. This allows us to propose a coding scheme to exploit untrusted relays in multi-user relay networks. We show that physical-layer network coding, especially compute-and-forward, is a key technology for simultaneous and secure communication of several users over an untrusted relay. First, we derive the achievable secrecy rate for the two-way relay channel. Then, we enhance this scenario to a multi-way relay channel with multiple antennas. We describe our implementation of the compute-and-forward framework with software-defined radio and demonstrate the practical feasibility. We show that it is possible to use the framework in real-life scenarios and demonstrate a transmission from two users to a relay. We gain valuable insights into a real transmission using the compute-and-forward framework. We discuss possible improvements of the current implementation and point out further work. / In dieser Arbeit untersuchen wir Netzwerkcodierung auf der Übertragungsschicht in einem Relay-Netzwerk, in dem L Quellen-Knoten Nachrichten zu K Senken-Knoten über M Relay-Knoten senden wollen. Der Fokus dieser Arbeit liegt auf der Informationsverarbeitung an den Relay-Knoten und dem Compute-and-Forward Framework. Es werden Nested Lattice Codes eingesetzt, welche die Eigenschaft besitzen, dass jede Linearkombination zweier Codewörter wieder ein gültiges Codewort ergibt. Dies ist eine Eigenschaft, die für die Netzwerkcodierung von entscheidender Bedeutung ist. Da die eigentliche Netzwerkcodierung auf der Übertragungsschicht stattfindet, werden die Netzwerkcodierungskoeffizienten von den Kanalrealisierungen bestimmt. Das Finden der optimalen Koeffizienten für gegebene Kanalrealisierungen ist ein nicht-triviales Optimierungsproblem. Wir schlagen in dieser Arbeit einen Algorithmus vor, welcher Netzwerkcodierungskoeffizienten findet, die in der höchsten Übertragungsrate an einem gewählten Relay resultieren. Die Lösung dieses Optimierungsproblems ist zunächst nur lokal, d. h. für dieses Relay, optimal. An jedem potentiellen Empfänger müssen ausreichend unabhängige Linearkombinationen vorhanden sein, um die einzelnen Nachrichten decodieren zu können. Ist dies nicht der Fall, kommt es zu Datenverlusten. Um dieses Problem zu umgehen, ohne dabei das Optimierungsproblem global lösen zu müssen, schlagen wir eine neue Strategie vor, welche den Lösungsraum an einem Relay soweit einschränkt, dass lineare Unabhängigkeit zwischen den decodierten Linearkombinationen an den Relays garantiert ist. Außerdem diskutieren wir den Einfluss von räumlicher Korrelation auf das Optimierungsproblem. Wir kombinieren die Netzwerkcodierung mit dem Konzept von Sicherheit auf der Übertragungsschicht, um ein Übertragungsschema zu entwickeln, welches es ermöglicht, mit Hilfe nicht-vertrauenswürdiger Relays zu kommunizieren. Wir zeigen, dass Compute-and-Forward ein wesentlicher Baustein ist, um solch eine sichere und simultane Übertragung mehrerer Nutzer zu gewährleisten. Wir starten mit dem einfachen Fall eines Relay-Kanals mit zwei Nutzern und erweitern dieses Szenario auf einen Relay-Kanal mit mehreren Nutzern und mehreren Antennen. Die Arbeit wird abgerundet, indem wir eine Implementierung des Compute-and-Forward Frameworks mit Software-Defined Radio demonstrieren. Wir zeigen am Beispiel von zwei Nutzern und einem Relay, dass sich das Framework eignet, um in realen Szenarien eingesetzt zu werden. Wir diskutieren mögliche Verbesserungen und zeigen Richtungen für weitere Forschungsarbeit auf.

The classical binary error correcting codes, and subspace codes for error correction in random network coding are two different forms of error control coding. We identify common features between these two forms and study the relations between them using the aid of lattices. Lattices are partial ordered sets where every pair of elements has a least upper bound and a greatest lower bound in the lattice. We shall demonstrate that many questions that connect these forms have a natural motivation from the viewpoint of lattices. We shall show that a lattice framework captures the notion of Singleton bound where the bound is on the size of the code as a function of its parameters. For the most part, we consider a special type of a lattice which has the geometric modular property. We will use a lattice framework to combine the two different forms. And then, in order to demonstrate the utility of this binding view, we shall derive a general version of Singleton bound. We will note that the Singleton bounds behave differently in certain respects because the binary coding framework is associated with a lattice that is distributive. We shall demonstrate that lack of distributive gives rise to a weaker bound. We show that Singleton bound for classical binary codes, subspace codes, rank metric codes and Ferrers diagram rank metric codes can be derived using a common technique. In the literature, Singleton bounds are derived for Ferrers diagram rank metric codes where the rank metric codes are linear. We introduce a generalized version of Ferrers diagram rank metric codes and obtain a Singleton bound for this version. Next, we shall prove a conjecture concerning the constraints of embedding a binary coding framework into a subspace framework. We shall prove a conjecture by Braun, Etzion and Vardy, which states that any such embedding which contains the full space in its range is constrained to have a particular size. Our proof will use a theorem due to Lovasz, a subspace counting theorem for geometric modular lattices, to prove the conjecture. We shall further demonstrate that any code that achieves the conjectured size must be of a particular type. This particular type turns out to be a natural distributive sub-lattice of a given geometric modular lattice.

Dans les réseaux traditionnels, la transmission de flux de données s'effectuaient par routage des paquets de la source vers le ou les destinataires. Le codage réseau (NC) permet aux nœuds intermédiaires du réseau d'effectuer des combinaisons linéaires des paquets de données qui arrivent à leurs liens entrants. Les opérations de codage ont lieu dans un corps de Galois de taille finie q. Aux destinataires, le décodage se fait par une élimination de Gauss des paquets codés-réseau reçus. Cependant, dans les réseaux sans fils, le codage réseau doit souvent faire face à des erreurs de transmission causées par le bruit, les effacements, et les interférences. Ceci est particulièrement problématique pour les applications temps réel, telle la transmission de contenus multimédia, où les contraintes en termes de délais d'acheminement peuvent aboutir à la réception d'un nombre insuffisant de paquets, et par conséquent à des difficultés à décoder les paquets transmis. Dans le meilleurs des cas, certains paquets arrivent à être décodés. Dans le pire des cas, aucun paquet ne peut être décodé.Dans cette thèse, nous proposons des schémas de codage conjoint source-réseau dont l'objectif est de fournir une reconstruction approximative de la source, dans des situations où un décodage parfait est impossible. L'idée consiste à exploiter la redondance de la source au niveau du décodeur afin d'estimer les paquets émis, même quand certains de ces paquets sont perdus après avoir subi un codage réseau. La redondance peut être soit naturelle, c'est-à-dire déjà existante, ou introduite de manière artificielle.Concernant la redondance artificielle, le codage à descriptions multiples (MDC) est choisi comme moyen d'introduire de la redondance structurée entre les paquets non corrélés. En combinant le codage à descriptions multiples et le codage réseau, nous cherchons à obtenir une qualité de reconstruction qui s'améliore progressivement avec le nombre de paquets codés-réseau reçus.Nous considérons deux approches différentes pour générer les descriptions. La première approche consiste à générer les descriptions par une expansion sur trame appliquée à la source avant la quantification. La reconstruction de données se fait par la résolution d'un problème d' optimisation quadratique mixte. La seconde technique utilise une matrice de transformée dans un corps de Galois donné, afin de générer les descriptions, et le décodage se fait par une simple éliminationde Gauss. Ces schémas sont particulièrement intéressants dans un contexte de transmission de contenus multimédia, comme le streaming vidéo, où la qualité s'améliore avec le nombre de descriptions reçues.Une seconde application de tels schémas consiste en la diffusion de données vers des terminaux mobiles à travers des canaux de transmission dont les conditions sont variables. Dans ce contexte, nous étudions la qualité de décodage obtenue pour chacun des deux schémas de codage proposés, et nous comparons les résultats obtenus avec ceux fournis par un schéma de codage réseau classique.En ce qui concerne la redondance naturelle, un scénario typique est celui d'un réseau de capteurs, où des sources géographiquement distribuées prélèvent des mesures spatialement corrélées. Nous proposons un schéma dont l'objectif est d'exploiter cette redondance spatiale afin de fournir une estimation des échantillons de mesures transmises par la résolution d'un problème d'optimisation quadratique à variables entières. La qualité de reconstruction est comparée à celle obtenue à travers un décodage réseau classique. / While network data transmission was traditionally accomplished via routing, network coding (NC) broke this rule by allowing network nodes to perform linear combinations of the upcoming data packets. Network operations are performed in a specific Galois field of fixed size q. Decoding only involves a Gaussian elimination with the received network-coded packets. However, in practical wireless environments, NC might be susceptible to transmission errors caused by noise, fading, or interference. This drawback is quite problematic for real-time applications, such as multimediacontent delivery, where timing constraints may lead to the reception of an insufficient number of packets and consequently to difficulties in decoding the transmitted sources. At best, some packets can be recovered, while in the worst case, the receiver is unable to recover any of the transmitted packets.In this thesis, we propose joint source-network coding and decoding schemes in the purpose of providing an approximate reconstruction of the source in situations where perfect decoding is not possible. The main motivation comes from the fact that source redundancy can be exploited at the decoder in order to estimate the transmitted packets, even when some of them are missing. The redundancy can be either natural, i.e, already existing, or artificial, i.e, externally introduced.Regarding artificial redundancy, we choose multiple description coding (MDC) as a way of introducing structured correlation among uncorrelated packets. By combining MDC and NC, we aim to ensure a reconstruction quality that improves gradually with the number of received network-coded packets. We consider two different approaches for generating descriptions. The first technique consists in generating multiple descriptions via a real-valued frame expansion applied at the source before quantization. Data recovery is then achieved via the solution of a mixed integerlinear problem. The second technique uses a correlating transform in some Galois field in order to generate descriptions, and decoding involves a simple Gaussian elimination. Such schemes are particularly interesting for multimedia contents delivery, such as video streaming, where quality increases with the number of received descriptions.Another application of such schemes would be multicasting or broadcasting data towards mobile terminals experiencing different channel conditions. The channel is modeled as a binary symmetric channel (BSC) and we study the effect on the decoding quality for both proposed schemes. Performance comparison with a traditional NC scheme is also provided.Concerning natural redundancy, a typical scenario would be a wireless sensor network, where geographically distributed sources capture spatially correlated measures. We propose a scheme that aims at exploiting this spatial redundancy, and provide an estimation of the transmitted measurement samples via the solution of an integer quadratic problem. The obtained reconstruction quality is compared with the one provided by a classical NC scheme.

We consider the problem of secure communications in a Gaussian two-way relay network where two nodes exchange confidential messages only via an untrusted relay. The relay is assumed to be honest but curious, i.e., an eavesdropper that conforms to the system rules and applies the intended relaying scheme. We analyze the achievable secrecy rates by applying network coding on the physical layer or the network layer and compare the results in terms of complexity, overhead, and efficiency. Further, we discuss the advantages and disadvantages of the respective approaches.

Preventing the success of active attacks is of essential importance for network coding since even the infiltration of one single corrupted data packet can jam large parts of the network. The existing approaches for network coding schemes preventing such pollution attacks can be divided into two categories: utilize cryptographic approaches or utilize redundancy similar to error correction coding. Within this paper, we compared both paradigms concerning efficiency of data transmission under various circumstances. Particularly, we considered an attacker of a certain strength as well as the influence of the generation size. The results are helpful for selecting a suitable approach for network coding taking into account both security against pollution attacks and efficiency.

In this thesis, we investigate physical-layer network coding in an L × M × K relay network, where L source nodes want to transmit messages to K sink nodes via M relay nodes. We focus on the information processing at the relay nodes and the compute-and-forward framework. Nested lattice codes are used, which have the property that every linear combination of codewords is a valid codeword. This property is essential for physical-layer network coding. Because the actual network coding occurs on the physical layer, the network coding coefficients are determined by the channel realizations. Finding the optimal network coding coefficients for given channel realizations is a non-trivial optimization problem. In this thesis, we provide an algorithm to find network coding coefficients that result in the highest data rate at a chosen relay. The solution of this optimization problem is only locally optimal, i.e., it is optimal for a particular relay. If we consider a multi-hop network, each potential receiver must get enough linear independent combinations to be able to decode the individual messages. If this is not the case, outage occurs, which results in data loss. In this thesis, we propose a new strategy for choosing the network coding coefficients locally at the relays without solving the optimization problem globally. We thereby reduce the solution space for the relays such that linear independence between their decoded linear combinations is guaranteed. Further, we discuss the influence of spatial correlation on the optimization problem. Having solved the optimization problem, we combine physical-layer network coding with physical-layer secrecy. This allows us to propose a coding scheme to exploit untrusted relays in multi-user relay networks. We show that physical-layer network coding, especially compute-and-forward, is a key technology for simultaneous and secure communication of several users over an untrusted relay. First, we derive the achievable secrecy rate for the two-way relay channel. Then, we enhance this scenario to a multi-way relay channel with multiple antennas. We describe our implementation of the compute-and-forward framework with software-defined radio and demonstrate the practical feasibility. We show that it is possible to use the framework in real-life scenarios and demonstrate a transmission from two users to a relay. We gain valuable insights into a real transmission using the compute-and-forward framework. We discuss possible improvements of the current implementation and point out further work. / In dieser Arbeit untersuchen wir Netzwerkcodierung auf der Übertragungsschicht in einem Relay-Netzwerk, in dem L Quellen-Knoten Nachrichten zu K Senken-Knoten über M Relay-Knoten senden wollen. Der Fokus dieser Arbeit liegt auf der Informationsverarbeitung an den Relay-Knoten und dem Compute-and-Forward Framework. Es werden Nested Lattice Codes eingesetzt, welche die Eigenschaft besitzen, dass jede Linearkombination zweier Codewörter wieder ein gültiges Codewort ergibt. Dies ist eine Eigenschaft, die für die Netzwerkcodierung von entscheidender Bedeutung ist. Da die eigentliche Netzwerkcodierung auf der Übertragungsschicht stattfindet, werden die Netzwerkcodierungskoeffizienten von den Kanalrealisierungen bestimmt. Das Finden der optimalen Koeffizienten für gegebene Kanalrealisierungen ist ein nicht-triviales Optimierungsproblem. Wir schlagen in dieser Arbeit einen Algorithmus vor, welcher Netzwerkcodierungskoeffizienten findet, die in der höchsten Übertragungsrate an einem gewählten Relay resultieren. Die Lösung dieses Optimierungsproblems ist zunächst nur lokal, d. h. für dieses Relay, optimal. An jedem potentiellen Empfänger müssen ausreichend unabhängige Linearkombinationen vorhanden sein, um die einzelnen Nachrichten decodieren zu können. Ist dies nicht der Fall, kommt es zu Datenverlusten. Um dieses Problem zu umgehen, ohne dabei das Optimierungsproblem global lösen zu müssen, schlagen wir eine neue Strategie vor, welche den Lösungsraum an einem Relay soweit einschränkt, dass lineare Unabhängigkeit zwischen den decodierten Linearkombinationen an den Relays garantiert ist. Außerdem diskutieren wir den Einfluss von räumlicher Korrelation auf das Optimierungsproblem. Wir kombinieren die Netzwerkcodierung mit dem Konzept von Sicherheit auf der Übertragungsschicht, um ein Übertragungsschema zu entwickeln, welches es ermöglicht, mit Hilfe nicht-vertrauenswürdiger Relays zu kommunizieren. Wir zeigen, dass Compute-and-Forward ein wesentlicher Baustein ist, um solch eine sichere und simultane Übertragung mehrerer Nutzer zu gewährleisten. Wir starten mit dem einfachen Fall eines Relay-Kanals mit zwei Nutzern und erweitern dieses Szenario auf einen Relay-Kanal mit mehreren Nutzern und mehreren Antennen. Die Arbeit wird abgerundet, indem wir eine Implementierung des Compute-and-Forward Frameworks mit Software-Defined Radio demonstrieren. Wir zeigen am Beispiel von zwei Nutzern und einem Relay, dass sich das Framework eignet, um in realen Szenarien eingesetzt zu werden. Wir diskutieren mögliche Verbesserungen und zeigen Richtungen für weitere Forschungsarbeit auf.