Efficient Decoding Algorithms for the Compute-and-Forward Strategy

We address in this paper decoding aspects of the Compute-and-Forward (CF) physical-layer network coding strategy. It is known that the original decoder for the CF is asymptotically optimal. However, its performance gap to optimal decoders in practical settings are still not known. In this work, we develop and assess the performance of novel decoding algorithms for the CF operating in the multiple access channel. For the fading channel, we analyze the ML decoder and develop a novel diophantine approximation-based decoding algorithm showed numerically to outperform the original CF decoder. For the Gaussian channel, we investigate the maximum a posteriori (MAP) decoder. We derive a novel MAP decoding metric and develop practical decoding algorithms proved numerically to outperform the original one

Cloud Compute-and-Forward with Relay Cooperation

We study a cloud network with M distributed receiving antennas and L users, which transmit their messages towards a centralized decoder (CD), where M>=L. We consider that the cloud network applies the Compute-and-Forward (C&F) protocol, where L antennas/relays are selected to decode integer equations of the transmitted messages. In this work, we focus on the best relay selection and the optimization of the Physical-Layer Network Coding (PNC) at the relays, aiming at the throughput maximization of the network. Existing literature optimizes PNC with respect to the maximization of the minimum rate among users. The proposed strategy maximizes the sum rate of the users allowing nonsymmetric rates, while the optimal solution is explored with the aid of the Pareto frontier. The problem of relay selection is matched to a coalition formation game, where the relays and the CD cooperate in order to maximize their profit. Efficient coalition formation algorithms are proposed, which perform joint relay selection and PNC optimization. Simulation results show that a considerable improvement is achieved compared to existing results, both in terms of the network sum rate and the players' profits.Comment: Submitted to IEEE Transactions on Wireless Communication

Energy Efficient, Cooperative Communication in Low-Power Wireless Networks

The increased interest in massive deployment of wireless sensors and network densification requires more innovation in low-latency communication across multi-hop networks. Moreover, the resource constrained nature of sensor nodes calls for more energy efficient transmission protocols, in order to increase the battery life of said devices. Therefore, it is important to investigate possible technologies that would aid in improving energy efficiency and decreasing latency in wireless sensor networks (WSN) while focusing on application specific requirements. To this end, and based on state of the art Glossy, a low-power WSN flooding protocol, this dissertation introduces two energy efficient, cooperative transmission schemes for low-power communication in WSNs, with the aim of achieving performance gains in energy efficiency, latency and power consumption. These approaches apply several cooperative transmission technologies such as physical layer network coding and transmit beamforming. Moreover, mathematical tools such as convex optimization and game theory are used in order to analytically construct the proposed schemes. Then, system level simulations are performed, where the proposed schemes are evaluated based on different criteria. First, in order to improve over all latency in the network as well as energy efficiency, MF-Glossy is proposed; a communication scheme that enables the simultaneous flooding of different packets from multiple sources to all nodes in the network. Using a communication-theoretic analysis, upper bounds on the performance of Glossy and MF-Glossy are determined. Further, simulation results show that MF-Glossy has the potential to achieve several-fold improvements in goodput and latency across a wide spectrum of network configurations at lower energy costs and comparable packet reception rates. Hardware implementation challenges are discussed as a step towards harnessing the potential of MF-Glossy in real networks, while focusing on key challenges and possible solutions. Second, under the assumption of available channel state information (CSI) at all nodes, centralized and distributed beamforming and power control algorithms are proposed and their performance is evaluated. They are compared in terms of energy efficiency to standard Glossy. Numerical simulations demonstrate that a centralized power control scheme can achieve several-fold improvements in energy efficiency over Glossy across a wide spectrum of network configurations at comparable packet reception rates. Furthermore, the more realistic scenario where CSI is not available at transmitting nodes is considered. To battle CSI unavailability, cooperation is introduced on two stages. First, cooperation between receiving and transmitting nodes is proposed for the process of CSI acquisition, where the receivers provide the transmitters with quantized (e.g. imperfect) CSI. Then, cooperation within transmitting nodes is proposed for the process of multi-cast transmit beamforming. In addition to an analytical formulation of the robust multi-cast beamforming problem with imperfect CSI, its performance is evaluated, in terms of energy efficiency, through numerical simulations. It is shown that the level of cooperation, represented by the number of limited feedback bits from receivers to transmitters, greatly impacts energy efficiency. To this end, the optimization problem of finding the optimal number of feedback bits B is formulated, as a programming problem, under QoS constraints of 5% maximum outage. Numerical simulations show that there exists an optimal number of feedback bits that maximizes energy efficiency. Finally, the effect of choosing cooperating transmitters on energy efficiency is studied, where it is shown that an optimum group of cooperating transmit nodes, also known as a transmit coalition, can be formed in order to maximize energy efficiency. The investigated techniques including optimum feedback bits and transmit coalition formation can achieve a 100% increase in energy efficiency when compared to state of the art Glossy under same operation requirements in very dense networks. In summary, the two main contributions in this dissertation provide insights on the possible performance gains that can be achieved when cooperative technologies are used in low-power wireless networks

Compute-and-Forward in Multi-User Relay Networks: Optimization, Implementation, and Secrecy

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