Cooperative Compute-and-Forward

We examine the benefits of user cooperation under compute-and-forward. Much like in network coding, receivers in a compute-and-forward network recover finite-field linear combinations of transmitters' messages. Recovery is enabled by linear codes: transmitters map messages to a linear codebook, and receivers attempt to decode the incoming superposition of signals to an integer combination of codewords. However, the achievable computation rates are low if channel gains do not correspond to a suitable linear combination. In response to this challenge, we propose a cooperative approach to compute-and-forward. We devise a lattice-coding approach to block Markov encoding with which we construct a decode-and-forward style computation strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information to aid receivers in decoding the integer combinations. Using our strategy, we show that cooperation offers a significant improvement both in the achievable computation rate and in the diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor

Lattice Coding for the Two-way Two-relay Channel

Lattice coding techniques may be used to derive achievable rate regions which outperform known independent, identically distributed (i.i.d.) random codes in multi-source relay networks and in particular the two-way relay channel. Gains stem from the ability to decode the sum of codewords (or messages) using lattice codes at higher rates than possible with i.i.d. random codes. Here we develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 2 3 4, where Node 1 and 4 simultaneously communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called "Re-distribution Transform". This allows nodes further down the line to again decode sums of lattice codewords. This transform is central to improving the achievable rates, and ensures that the messages traveling in each of the two directions fully utilize the relay's power, even under asymmetric channel conditions. All decoders are lattice decoders and only a single nested lattice codebook pair is needed. The symmetric rate achieved by the proposed lattice coding scheme is within 0.5 log 3 bit/Hz/s of the symmetric rate capacity.Comment: submitted to IEEE Transactions on Information Theory on December 3, 201

Nomographic Functions: Efficient Computation in Clustered Gaussian Sensor Networks

In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rather to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.Comment: to appear in IEEE Transactions on Wireless Communication

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

Towards Massive Connectivity Support for Scalable mMTC Communications in 5G networks

The fifth generation of cellular communication systems is foreseen to enable a multitude of new applications and use cases with very different requirements. A new 5G multiservice air interface needs to enhance broadband performance as well as provide new levels of reliability, latency and supported number of users. In this paper we focus on the massive Machine Type Communications (mMTC) service within a multi-service air interface. Specifically, we present an overview of different physical and medium access techniques to address the problem of a massive number of access attempts in mMTC and discuss the protocol performance of these solutions in a common evaluation framework

Cooperative Strategies for Near-Optimal Computation in Wireless Networks

Computation problems, such as network coding and averaging consen- sus, have become increasingly central to the study of wireless networks. Network coding, in which intermediate terminals compute and forward functions of others’ messages, is instrumental in establishing the capacity of multicast networks. Averaging consensus, in which terminals compute the mean of others’ measurements, is a canonical building block of dis- tributed estimation over sensor networks. Both problems, however, are typically studied over graphical networks, which abstract away the broad- cast and superposition properties fundamental to wireless propagation. The performance of computation in realistic wireless environments, there- fore, remains unclear. In this thesis, I seek after near-optimal computation strategies under realistic wireless models. For both network coding and averaging con- sensus, cooperative communications plays a key role. For network cod- ing, I consider two topologies: a single-layer network in which users may signal cooperatively, and a two-transmitter, two-receiver network aided by a dedicated relay. In the former topology, I develop a decode-and- forward scheme based on a linear decomposition of nested lattice codes. For a network having two transmitters and a single receiver, the proposed scheme is optimal in the diversity-multiplexing tradeo↵; otherwise it pro- vides significant rate gains over existing non-cooperative approaches. In the latter topology, I show that an amplify-and-forward relay strategy is optimal almost everywhere in the degrees-of-freedom. Furthermore, for symmetric channels, amplify-and-forward achieves rates near capacity for a non-trivial set of channel gains. For averaging consensus, I consider large networks of randomly-placed nodes. Under a path-loss wireless model, I characterize the resource de- mands of consensus with respect to three metrics: energy expended, time elapsed, and time-bandwidth product consumed. I show that existing con- sensus strategies, such as gossip algorithms, are nearly order optimal in the energy expended but strictly suboptimal in the other metrics. I propose a new consensus strategy, tailored to the wireless medium and cooperative in nature, termed hierarchical averaging. Hierarchical averaging is nearly order optimal in all three metrics for a wide range of path-loss exponents. Finally, I examine consensus under a simple quantization model, show- ing that hierarchical averaging achieves a nearly order-optimal tradeo↵ between resource consumption and estimation accuracy

Low-cost Interference Mitigation and Relay Processing for Cooperative DS-CDMA Systems

In wireless communications, propagation aspects such as fading, shadowing and path loss are the major constraints that seriously limit the overall performance of systems. Indeed, severe fading has a detrimental effect on the received signals and can lead to a degradation of the transmission of information and the reliability of the network. In this case, diversity techniques are introduced in order to mitigate fading. Among various kinds of diversity techniques, cooperative diversity with relaying nodes is a modern technique that has been widely considered in recent years as an effective tool to deal with this problem. Several cooperative protocols have been proposed in the literature, and among the most effective ones are Amplify-and-Forward (AF) and Decode-and-Forward (DF). Cooperative diversity can be combined with direct sequence code division multiple access (DS-CDMA) systems to further enhance the information security. However, due to the multiple access interference (MAI) that arises from nonorthogonal received waveforms in the DS-CDMA systems, the system performance may easily be affected. To deal with this issue, novel multiuser detection (MUD) technique is introduced as a useful relay processing strategy for the uplink of cooperative DS-CDMA systems. Apart from that, distributed space-time coding (DSTC) is another effective approach that can be combined with cooperative diversity to further improve the transmission performance. Moreover, in order to increase the throughput of the cooperative DS-CDMA network, physical-layer network coding (PNC) scheme is then adopted together with the cooperative DS-CDMA network. Clearly, better performance gain and lower power consumption can be obtained when appropriate relaying strategies are applied

Hardware Implementation of Fixed-Point Decoder for Low-Density Lattice Codes

Low-density lattice codes (LDLCs) are a special class of lattice codes that can be decoded efficiently using iterative decoding and approach the capacity of the additive white Gaussian noise (AWGN) channel. The construction and intended applications are substantially different from that of more familiar error-correcting codes such as low-density parity check (LDPC) codes, Polar, and Turbo codes. Lattice codes in general have shown great theoretical promise to mitigate interference, possibly leading to significantly higher rates between users in multi-user networks. Research on LDLCs has concentrated on demonstrating the theoretically achievable performance limits of LDLCs, and until now there has been no reported hardware implementation, mainly due to the complexity of message-passing for LDLC decoding. This thesis contributes to the hardware implementation of the LDLC decoding. We present several fixed-point decoder implementations covering different parts of the architectural design space, on a field-programmable gate array (FPGA) device. We first present the FPGA implementation of a fixed-point arithmetic LDLC decoder where the Gaussian mixture messages that are exchanged during the iterative decoding process are approximated to a single Gaussian. A detailed quantization study is performed to find the minimum number of bits required for the fixed-point decoder implementation to attain a frame-error-rate (FER) performance similar to floating-point. Efficient numerical methods are used to approximate the non-linear functions required in the decoder. A two-node serial LDLC decoder is implemented on an Intel Arria 10 FPGA as a hardware proof-of-concept attaining a throughput of 440 Ksymbols/sec at high signal-to-noise ratio (SNR). This throughput is obtained at clock frequency of 125 MHz and for a block length of 1000. By exploiting the inherent parallelism of iterative decoding, several parallel message processing blocks are then used to improve the throughput by a factor of 13x. Finally, we propose a pipelined architecture where the decoder achieves a throughput of 10.5 Msymbols/sec, that is, ~24x improvement over the serial decoder. Then, we implement a multi-Gaussian decoder where the Gaussian mixture messages exchanged during the decoding process have two components. We develop efficient techniques to reduce the decoder complexity for hardware implementation, e.g., selecting the strongest component from the Gaussian mixture as the final decision in iterative decoding, and a simplified method for coefficient computation during the product operation at the variable nodes. With a thorough quantization analysis and applying methods devised to approximate the non-linear functions, we design the multi-Gaussian decoders in fixed point arithmetic. We first implemented a serial architecture with a single check node and a single variable node. Then, a partially parallel architecture with a single check node and a variable node message processing block with two-stage pipelining is implemented to achieve an effective parallelism of 5 variable nodes. The pipelined architecture achieves an improvement of ~0.75 dB in decoding performance over the single Gaussian decoder of degree 3 with an overall design throughput of 550 Ksymbols/sec. In the final part of the thesis, we further explore the design space and develop complex LDLC decoder designs for higher degrees. We characterize the decoding performance of these decoders and present the design throughputs for different architectures on the target FPGA. Based on these results, we provide insights that will help users to select the most suitable LDLC decoder for a particular application. However this is attained with additional hardware cost and reduced design throughput. A single-Gaussian decoder of degree 7 achieved an FER improvement of 0.75 dB over a single-Gaussian decoder of degree 3 with a throughput of 3.03 Msymbols/sec. The multi-Gaussian Gaussian decoder of degree 7 (with two components in the Gaussian mixture) attains 1.75 dB improvement in FER over the multi-Gaussian decoder of degree 3, and its overall design throughput is ~84 Ksymbols/sec. From a broader perspective, the LDLC decoders with higher degrees and larger mixture messages provide a significant improvement in decoding performance. For ultra-reliable applications, a multi-Gaussian decoder of degree 7 is most suitable while for a very high throughput requirement single-Gaussian decoder of degree 3 is the best choice. We also characterize the performance of multi-Gaussian decoders where the Gaussian mixture messages contain more than two components. Based on the results, the multi- Gaussian decoder with mixture messages that contain 5 components gain approximately ~0.1 - 0.2 dB (for degree 3 and 7) and ~0.3 dB (for degree 5) over multi-Gaussian decoder where mixture messages have only two components

Caching and Distributed Storage:Models, Limits and Designs

A simple task of storing a database or transferring it to a different point via a communication channel turns far more complex as the size of the database grows large. Limited bandwidth available for transmission plays a central role in this predicament. In two broad contexts, Content Distribution Networks (CDN) and Distributed Storage Systems (DSS), the adverse effect of the growing size of the database on the transmission bandwidth can be mitigated by exploiting additional storage units. Characterizing the optimal tradeoff between the transmission bandwidth and the storage size is the central quest to numerous works in the recent literature, including this thesis. In a DSS, individual servers fail routinely and must be replicated by downloading data from the remaining servers, a task referred to as the repair process. To render this process of repairing failed servers more straightforward and efficient, various forms of redundancy can be introduced in the system. One of the benchmarks by which the reliability of a DSS is measured is availability, which refers to the number of disjoint sets of servers that can help to repair any failed server. We study the interaction of this parameter with the amount of traffic generated during the repair process (the repair bandwidth) and the storage size. In particular, we propose a novel DSS architecture which can achieve much smaller repair bandwidth for the same availability, compared to the state of the art. In the context of CDNs, the network can be highly congested during certain hours of the day and almost idle at other times. This variability of traffic can be reduced by utilizing local storage units that prefetch the data while the network is idle. This approach is referred to as caching. In this thesis we analyze a CDN that has access to independent data from various content providers. We characterize the best caching strategy in terms of the aggregate peak traffic under the constraint that coding across contents from different libraries is prohibited. Furthermore we prove that under certain set of conditions this restriction is without loss of optimality