We consider a communication system where two transmitters wish to exchange information through a central relay. The data is assumed to be transmitted over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. It has been shown that using lattice codes and lattice decoding, a rate of 1/2 log_2(1/2 plus snr) can be obtained asymptotically, which is essentially optimal at high SNR. However, there has been a lack of practical encoding/decoding schemes for the above mentioned system. We address this issue in this thesis by developing encoding/decoding strategies for the bidirectional relaying system using low-dimensional lattice codes. Our efforts are aimed at developing coding schemes which possess low computational complexity while at the same time providing good performance. We demonstrate two schemes using low-dimensional lattice codes. Both these schemes have their own advantages and are suitable for different classes of lattice codes. The two schemes are tested with different lattices and their performance is compared to that of other schemes for bidirectional relays. The first scheme is termed as demodulate and forward and it essentially consists of performing optimal estimation at the relay. It is primarily implemented with lattice codes of low rate and possesses low decoding complexity. When used with a two-dimensional hexagonal lattice, it achieves a gain of around 3.5 dB in comparison to other schemes like Analog network coding. The second scheme is the sphere decoding scheme which has been implemented with high-rate lattice codes. The sphere decoder is a low-complexity decoder which is used for decoding to a lattice point at the relay. We observe that as the dimensionality of the lattice code is increased, the performance of the sphere decoder for the bidirectional relay gets consistently better. The sphere decoder is also used at high SNR for those instances in which the low density lattice code(LDLC) decoder makes an error and it is found that the sphere decoder can correct around 90 percent of these errors at an SNR of 9.75 dB.

A family of low-density lattice codes (LDLC) is studied based on Construction-A for lattices. The family of Construction-A codes is already known to contain a large capacity-achieving subset. Parallels are drawn between coset non-binary low-density parity-check (LDPC) codes and nested low-density Construction-A lattices codes. Most of the related research in LDPC domain assumes optimal power allocation to encoded codeword. The source coding problem of mapping message to power optimal codeword for any LDPC code is in general, NP-hard. In this thesis, we present a novel method for encoding and decoding lattice based on non-binary LDPC codes using message-passing algorithms. / text

With the usage of biometrics becoming commonly used in a variety of applications, keeping those biometrics private and secure is an important issue. Indeed, the convenience of using biometrics for authentication is counteracted by the fact that they cannot easily be modified or changed. This can have dire consequences to a person if their biometrics are leaked. In the past decades, various techniques have been proposed to solve this problem. Such techniques range from using and storing randomized templates, using homomorphic encryption, or using biometric encryption techniques such as fuzzy extractors. Fuzzy extractors are a construction that allows the extraction of cryptographic keys from noisy data like biometrics. The key can then be rebuilt from some helper data and another biometric, provided that it is similar enough to the biometrics used to generate the key. This can be achieved through various approaches like the use of a quantizer or an error correcting code. In this thesis, we consider specifically fuzzy extractors for facial images. The first part of this thesis focuses on improving the security, privacy and performance of the extractor for faces first proposed by Sutcu et al. Our improvements make their construction more resistant to partial and total leaks of secure information, as well as improve the performance in a biometric authentication setting. The second part looks at using low density lattice codes (LDLC) as a quantizer in the fuzzy extractor, instead of using component based quantization. Although LDLC have been proposed as a quantizer for a general fuzzy extractor, they have yet to be used or tested for continuous biometrics like face images. We present a construction for a fuzzy extractor scheme using LDLC and we analyze its performance on a publicly available data set of images. Using an LDLC quantizer on this data set has lower accuracy than the improved scheme from the first part of this thesis. On the other hand, the LDLC scheme performs better when the inputs have additive white Gaussian noise (AWGN), as we show through simulated data. As such, we expect it to perform well in general on data and biometrics with variance akin to a AWGN channel.

Next-generation wireless communication systems will need to contend with many active mobile devices, each of which will require a very high data rate. To cope with this growing demand, network deployments are becoming denser, leading to higher interference between active users. Conventional architectures aim to mitigate this interference through careful design of signaling and scheduling protocols. Unfortunately, these methods become less effective as the device density increases. One promising option is to enable cellular basestations (i.e., cell towers) to jointly process their received signals for decoding users’ data packets as well as to jointly encode their data packets to the users. This joint processing architecture is often enabled by a cloud radio access network that links the basestations to a central processing unit via dedicated connections. One of the main contributions of this thesis is a novel end-to-end communications architecture for cloud radio access networks as well as a detailed comparison to prior approaches, both via theoretical bounds and numerical simulations. Recent work has that the following high-level approach has numerous advantages: each basestation quantizes its observed signal and sends it to the central processing unit for decoding, which in turn generates signals for the basestations to transmit, and sends them quantized versions. This thesis follows an integer-forcing approach that uses the fact that, if codewords are drawn from a linear codebook, then their integer-linear combinations are themselves codewords. Overall, this architecture requires integer-forcing channel coding from the users to the central processing unit and back, which handles interference between the users’ codewords, as well as integer-forcing source coding from the basestations to the central processing unit and back, which handles correlations between the basestations’ analog signals. Prior work on integer-forcing has proposed and analyzed channel coding strategies as well as a source coding strategy for the basestations to the central processing unit, and this thesis proposes a source coding strategy for the other direction. Iterative algorithms are developed to optimize the parameters of the proposed architecture, which involve real-valued beamforming and equalization matrices and integer-valued coefficient matrices in a quadratic objective. Beyond the cloud radio setting, it is argued that the integer-forcing approach is a promising framework for interference alignment between multiple transmitter-receiver pairs. In this scenario, the goal is to align the interfering data streams so that, from the perspective of each receiver, there seems to be only a signal receiver. Integer-forcing interference alignment accomplishes this objective by having each receiver recover two linear combinations that can then be solved for the desired signal and the sum of the interference. Finally, this thesis investigates the impact of channel coherence on the integer-forcing strategy via numerical simulations.

The Pressure Tube Super Critical Water Reactor (PT-SCWR) is a design with a light water coolant operating at 25 MPa above the thermodynamic critical pressure, with a separated low pressure and temperature moderator, facilitated by a High E ciency Channel consisting of a pressure tube and a porous ceramic insulator tube. The 2011 AECL reference design is considered along with a 2012 benchmark. In the 2011 reference design the coolant is permitted to ow through the insulator. The insulator region has a temperature gradient from 881 K at the inner liner tube to 478 K at the pressure tube wall. The density of light water varies by an order of magnitude depending on the local enthalpy of the uid. The lateral coolant density is estimated as a radial function at ve axial positions with the lattice physics codes WIMS-AECL and Serpent. The lateral coolant density variations in the insulator region of the PT-SCWR cause strong reactivity and CVR e ects which vary heavily on axial location due to the changes in the estimated mass of coolant and the physical relocation of the coolant closer to the moderator, as the coolant is estimated to be least dense closer to the fuel region of the coolant ow. The beta version of Serpent 2 is used to explore the lateral coolant densities in the subchannel region of the insulator in the 2012 version of the PT-SCWR. A more advanced coolant density analysis with FLUENT is used to estimate the subchannel coolant density variation, which is linked to SERPENT 2s multi-physics interface, allowing the lattice code to measure the sensitivity of the model to the analysis of the subchannels. This analysis increases the reactivity of the PT-SCWR through the displacement of the coolant. Serpent 2 is accepted as a valid lattice code for PT-SCWR analysis. / Thesis / Master of Applied Science (MASc)

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.

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.

Bandlimited optical intensity channels, arising in applications such as indoor infrared communications and visible light communications (VLC), require that all signals satisfy a bandwidth constraint as well as average, peak and non-negative amplitude constraints. However, the signaling designed for conventional radio frequency (RF) electrical channels cannot be applied directly, since they take energy constraints into consideration instead of amplitude constraints. In addition, conventional transmission techniques optimized for broad-band optical channels such as fiber optics, terrestrial/satellite-to-satellite free-space optical (FSO) communications are typically not bandwidth efficient. In this thesis, a two-dimensional signal space for bandlimited optical intensity channels is presented. A novel feature of this model is that the non-negativity and peak amplitude constraints are relaxed. The signal space parameterizes the likelihood of a negative or peak amplitude excursions in the output. Although the intensity channel only supports non-negative amplitudes, the impact of clipping on system performance is shown to be negligible if the likelihood of negative amplitude excursion is small enough. For a given signal space, a tractable approximation approach using a finite series is applied to accurately compute the likelihood of clipping under average and peak optical power constraints. The uncoded asymptotic optical power and spectral efficiencies using two-dimensional lattice constellations are computed. The Monte-Carlo (MC) simulation results show that for a given average or peak optical power, schemes designed in the presented signal space haver higher spectral efficiency than M-ary pulse amplitude modulation (PAM) using previously established techniques. / Thesis / Master of Applied Science (MASc)

Channel coding has been largely used for the purpose of improving error performance on a communications system. Typical methods based on added redundancy allow for error detection and correction, this improvement however comes at a cost of bandwidth. This thesis focuses on channel coding for the bandwidth-limited channel where no bandwidth expansion is allowed. We first discuss the idea of coding for the bandwidth-limited channel as seen from the signal space point of view where the purpose of coding is to maximize the Euclidian distance between constellation points without increasing the total signal power and under the condition that no extra bits can be added. We then see the problem from another angle and identify the tradeoffs related to bandwidth and error performance. This thesis intends to find a simple way of achieving an improvement in error performance for the bandwidth-limited channel without the use of lattice codes or trellis-coded modulation. The proposed system is based on convolutional coding followed by multilevel transmission. It achieved a coding gain of 2 dB on Eb/No or equivalently, a coding gain of approximately 2.7 dB on SNRnorm without increase in bandwidth. This coding gain is better than that obtained by a more sophisticated lattice code Gosset E8 at the same error rate.

In the last decade, there has been an explosive growth in different applications of wireless technology, due to users' increasing expectations for multi-media services. With the current trend, the present systems will not be able to handle the required data traffic. Lattice codes have attracted considerable attention in recent years, because they provide high data rate constellations. In this thesis, the applications of implementing lattice codes in different communication systems are investigated. The thesis is divided into two major parts. Focus of the first part is on constellation shaping and the problem of lattice labeling. The second part is devoted to the lattice decoding problem. In constellation shaping technique, conventional constellations are replaced by lattice codes that satisfy some geometrical properties. However, a simple algorithm, called lattice labeling, is required to map the input data to the lattice code points. In the first part of this thesis, the application of lattice codes for constellation shaping in Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Input Multi-Output (MIMO) broadcast systems are considered. In an OFDM system a lattice code with low Peak to Average Power Ratio (PAPR) is desired. Here, a new lattice code with considerable PAPR reduction for OFDM systems is proposed. Due to the recursive structure of this lattice code, a simple lattice labeling method based on Smith normal decomposition of an integer matrix is obtained. A selective mapping method in conjunction with the proposed lattice code is also presented to further reduce the PAPR. MIMO broadcast systems are also considered in the thesis. In a multiple antenna broadcast system, the lattice labeling algorithm should be such that different users can decode their data independently. Moreover, the implemented lattice code should result in a low average transmit energy. Here, a selective mapping technique provides such a lattice code. Lattice decoding is the focus of the second part of the thesis, which concerns the operation of finding the closest point of the lattice code to any point in N-dimensional real space. In digital communication applications, this problem is known as the integer least-square problem, which can be seen in many areas, e.g. the detection of symbols transmitted over the multiple antenna wireless channel, the multiuser detection problem in Code Division Multiple Access (CDMA) systems, and the simultaneous detection of multiple users in a Digital Subscriber Line (DSL) system affected by crosstalk. Here, an efficient lattice decoding algorithm based on using Semi-Definite Programming (SDP) is introduced. The proposed algorithm is capable of handling any form of lattice constellation for an arbitrary labeling of points. In the proposed methods, the distance minimization problem is expressed in terms of a binary quadratic minimization problem, which is solved by introducing several matrix and vector lifting SDP relaxation models. The new SDP models provide a wealth of trade-off between the complexity and the performance of the decoding problem.