I propose a new communications scheme where signature signals are used to carry digital data by suitably modulating the signal parameters with information bits. One possible application for the proposed scheme is in underwater acoustic (UWA) communications; with this motivation, I demonstrate how it can be applied in UWA communications. In order to do that, I exploit existing parameterized models for mammalian sounds by using them as signature signals. Digital data is transmitted by mapping vectors of information bits to a carefully designed set of parameters with values obtained from the biomimetic signal models. To complete the overall system design, I develop appropriate receivers taking into account the specific UWA channel models. I present some numerical results from the analysis of data recorded during the Kauai Acomms MURI 2011 (KAM11) UWA communications experiment.

It is shown that the proposed communication scheme results in approximate channel models with amplitude-limited inputs and signal-dependent additive noise. Motivated by this observation, I study capacity of amplitude-limited channels under different transmission scenarios. Specifically, I consider fading channels, signal-dependent additive Gaussian noise channels, multiple-input multiple-output (MIMO) systems and parallel Gaussian channels under peak power constraints.

I also consider practical channel coding problems for channels with signal-dependent noise. I consider two specific models; signal-dependent additive Gaussian noise channels and Z-channels which serve as binary-input binary-output approximations to the Gaussian case. I propose a new upper bound on the probability of error, and utilize it for design of codes. I illustrate the tightness of the derived bounds and the performance of the designed codes via examples.

The recent proposal of two-way relaying has attracted much attention due to its promising features for many practical scenarios. Hereby, two users communicate simultaneously in both directions to exchange their messages with the help of a relay node. This doctoral study investigates various aspects of two-way relaying. Specifically, the issue of asynchronism, lack of channel knowledge, transmission of correlated sources and multi-way relaying techniques involving multiple users are explored.

With the motivation of developing enabling techniques for two-way relay (TWR) channels experiencing excessive synchronization errors, two conceptually-different schemes are proposed to accommodate any relative misalignment between the signals received at any node. By designing a practical transmission/detection mechanism based on orthogonal frequency division multiplexing (OFDM), the proposed schemes perform significantly better than existing competing solutions. In a related direction, differential modulation is implemented for asynchronous TWR systems that lack the channel state information (CSI) knowledge. The challenge in this problem compared to the conventional point-to-point counterpart arises not only from the asynchrony but also from the existence of an interfering signal. Extensive numerical examples, supported by analytical work, are given to demonstrate the advantages of the proposed schemes.

Other important issues considered in this dissertation are related to the extension of the two-way relaying scheme to the multiple-user case, known as the multi-way relaying. First, a distributed source coding solution based on Slepian-Wolf coding is proposed to compress correlated messages close to the information theoretical limits in the context of multi-way relay (MWR) channels. Specifically, the syndrome approach based on low-density parity-check (LDPC) codes is implemented. A number of relaying strategies are considered for this problem offering a tradeoff between performance and complexity. The proposed solutions have shown significant improvements compared to the existing ones in terms of the achievable compression rates. On a different front, a novel approach to channel coding is proposed for the MWR channel based on the implementation of nested codes in a distributed manner. This approach ensures that each node decodes the messages of the other users without requiring complex operations at the relay, and at the same time, providing substantial benefits compared to the traditional routing solution.

There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed.

Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels.

Practical communication systems are subject to errors due to imperfect time alignment among the communicating nodes. Timing errors can occur in different forms depending on the underlying communication scenario. This doctoral study considers two different classes of asynchronous systems; point-to-point (P2P) communication systems with synchronization errors, and asynchronous cooperative systems. In particular, the focus is on an information theoretic analysis for P2P systems with synchronization errors and developing new signaling solutions for several asynchronous cooperative communication systems. The first part of the dissertation presents several bounds on the capacity of the P2P systems with synchronization errors. First, binary insertion and deletion channels are considered where lower bounds on the mutual information between the input and output sequences are computed for independent uniformly distributed (i.u.d.) inputs. Then, a channel suffering from both synchronization errors and additive noise is considered as a serial concatenation of a synchronization error-only channel and an additive noise channel. It is proved that the capacity of the original channel is lower bounded in terms of the synchronization error-only channel capacity and the parameters of both channels. On a different front, to better characterize the deletion channel capacity, the capacity of three independent deletion channels with different deletion probabilities are related through an inequality resulting in the tightest upper bound on the deletion channel capacity for deletion probabilities larger than 0.65. Furthermore, the first non-trivial upper bound on the 2K-ary input deletion channel capacity is provided by relating the 2K-ary input deletion channel capacity with the binary deletion channel capacity through an inequality. The second part of the dissertation develops two new relaying schemes to alleviate asynchronism issues in cooperative communications. The first one is a single carrier (SC)-based scheme providing a spectrally efficient Alamouti code structure at the receiver under flat fading channel conditions by reducing the overhead needed to overcome the asynchronism and obtain spatial diversity. The second one is an orthogonal frequency division multiplexing (OFDM)-based approach useful for asynchronous cooperative systems experiencing excessive relative delays among the relays under frequency-selective channel conditions to achieve a delay diversity structure at the receiver and extract spatial diversity.

Insertion and deletion errors represent an important category of channel impairments. Despite their importance and much work over the years, channels with such impairments are far from being fully understood as they proved to be difficult to analyze. In this dissertation, a promising coding scheme is investigated over independent and identically distributed (i.i.d.) insertion/deletion channels, i.e., interleaved concatenation of an outer low-density parity-check (LDPC) code with error-correction capabilities and an inner marker code for synchronization purposes. Marker code structures which offer the highest achievable rates are found with standard bit-level synchronization is performed. Then, to exploit the correlations in the likelihoods corresponding to different transmitted bits, a novel symbol-level synchronization algorithm that works on groups of consecutive bits is introduced. Extrinsic information transfer (EXIT) charts are also utilized to analyze the convergence behavior of the receiver, and to design LDPC codes with degree distributions matched to these channels. The next focus is on segmented deletion channels. It is first shown that such channels are information stable, and hence their channel capacity exists. Several upper and lower bounds are then introduced in an attempt to understand the channel capacity behavior. The asymptotic behavior of the channel capacity is also quantified when the average bit deletion rate is small. Further, maximum-a-posteriori (MAP) based synchronization algorithms are developed and specific LDPC codes are designed to match the channel characteristics. Finally, in addition to binary substitution errors, coding schemes and the corresponding detection algorithms are also studied for several other models with synchronization errors, including inter-symbol interference (ISI) channels, channels with multiple transmit/receive elements and multi-user communication systems.

This dissertation considers two different kinds of two-hop multiple-input multiple-output (MIMO) relay networks with beamforming (BF). First, "one-way" amplify-and-forward (AF) and decode-and-forward (DF) MIMO BF relay networks are considered, in which the relay amplifies or decodes the received signal from the source and forwards it to the destination, respectively, where all nodes beamform with multiple antennas to obtain gains in performance with reduced power consumption. A direct link from source to destination is included in performance analysis. Novel systematic upper-bounds and lower-bounds to average bit or symbol error rates (BERs or SERs) are proposed. Second, "two-way" AF MIMO BF relay networks are investigated, in which two sources exchange their data through a relay, to improve the spectral efficiency compared with one-way relay networks. Novel unified performance analysis is carried out for five different relaying schemes using two, three, and four time slots in sum-BER, the sum of two BERs at both sources, in two-way relay networks with and without direct links. For both kinds of relay networks, when any node is beamforming simultaneously to two nodes (i.e. from source to relay and destination in one-way relay networks, and from relay to both sources in two-way relay networks), the selection of the BF coefficients at a beamforming node becomes a challenging problem since it has to balance the needs of both receiving nodes. Although this "BF optimization" is performed for BER, SER, and sum-BER in this dissertation, the solution for optimal BF coefficients not only is difficult to implement, it also does not lend itself to performance analysis because the optimal BF coefficients cannot be expressed in closed-form. Therefore, the performance of optimal schemes through bounds, as well as suboptimal ones such as strong-path BF, which beamforms to the stronger path of two links based on their received signal-to-noise ratios (SNRs), is provided for BERs or SERs, for the first time. Since different channel state information (CSI) assumptions at the source, relay, and destination provide different error performance, various CSI assumptions are also considered.

Complex dynamical systems consisting interacting dynamical units are ubiquitous in nature and society. Predicting and reconstructing nonlinear dynamics of units and the complex interacting networks among them serves the base for the understanding of a variety of collective dynamical phenomena. I present a general method to address the two outstanding problems as a whole based solely on time-series measurements. The method is implemented by incorporating compressive sensing approach that enables an accurate reconstruction of complex dynamical systems in terms of both nodal equations that determines the self-dynamics of units and detailed coupling patterns among units. The representative advantages of the approach are (i) the sparse data requirement which allows for a successful reconstruction from limited measurements, and (ii) general applicability to identical and nonidentical nodal dynamics, and to networks with arbitrary interacting structure, strength and sizes. Another two challenging problem of significant interest in nonlinear dynamics: (i) predicting catastrophes in nonlinear dynamical systems in advance of their occurrences and (ii) predicting the future state for time-varying nonlinear dynamical systems, can be formulated and solved in the framework of compressive sensing using only limited measurements. Once the network structure can be inferred, the dynamics behavior on them can be investigated, for example optimize information spreading dynamics, suppress cascading dynamics and traffic congestion, enhance synchronization, game dynamics, etc. The results can yield insights to control strategies design in the real-world social and natural systems. Since 2004, there has been a tremendous amount of interest in graphene. The most amazing feature of graphene is that there exists linear energy-momentum relationship when energy is low. The quasi-particles inside the system can be treated as chiral, massless Dirac fermions obeying relativistic quantum mechanics. Therefore, the graphene provides one perfect test bed to investigate relativistic quantum phenomena, such as relativistic quantum chaotic scattering and abnormal electron paths induced by klein tunneling. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.

Underwater acoustic communications face significant challenges unprecedented in radio terrestrial communications including long multipath delay spreads, strong Doppler effects, and stringent bandwidth requirements. Recently, multi-carrier communications based on orthogonal frequency division multiplexing (OFDM) have seen significant growth in underwater acoustic (UWA) communications, thanks to their well well-known robustness against severely time-dispersive channels. However, the performance of OFDM systems over UWA channels significantly deteriorates due to severe intercarrier interference (ICI) resulting from rapid time variations of the channel. With the motivation of developing enabling techniques for OFDM over UWA channels, the major contributions of this thesis include (1) two effective frequencydomain equalizers that provide general means to counteract the ICI; (2) a family of multiple-resampling receiver designs dealing with distortions caused by user and/or path specific Doppler scaling effects; (3) proposal of using orthogonal frequency division multiple access (OFDMA) as an effective multiple access scheme for UWA communications; (4) the capacity evaluation for single-resampling versus multiple-resampling receiver designs. All of the proposed receiver designs have been verified both through simulations and emulations based on data collected in real-life UWA communications experiments. Particularly, the frequency domain equalizers are shown to be effective with significantly reduced pilot overhead and offer robustness against Doppler and timing estimation errors. The multiple-resampling designs, where each branch is tasked with the Doppler distortion of different paths and/or users, overcome the disadvantages of the commonly-used single-resampling receivers and yield significant performance gains. Multiple-resampling receivers are also demonstrated to be necessary for UWA OFDMA systems. The unique design effectively mitigates interuser interference (IUI), opening up the possibility to exploit advanced user subcarrier assignment schemes. Finally, the benefits of the multiple-resampling receivers are further demonstrated through channel capacity evaluation results.

There are many wireless communication and networking applications that require high transmission rates and reliability with only limited resources in terms of bandwidth, power, hardware complexity etc.. Real-time video streaming, gaming and social networking are a few such examples. Over the years many problems have been addressed towards the goal of enabling such applications; however, significant challenges still remain, particularly, in the context of multi-user communications. With the motivation of addressing some of these challenges, the main focus of this dissertation is the design and analysis of capacity approaching coding schemes for several (wireless) multi-user communication scenarios. Specifically, three main themes are studied: superposition coding over broadcast channels, practical coding for binary-input binary-output broadcast channels, and signalling schemes for two-way relay channels. As the first contribution, we propose an analytical tool that allows for reliable comparison of different practical codes and decoding strategies over degraded broadcast channels, even for very low error rates for which simulations are impractical. The second contribution deals with binary-input binary-output degraded broadcast channels, for which an optimal encoding scheme that achieves the capacity boundary is found, and a practical coding scheme is given by concatenation of an outer low density parity check code and an inner (non-linear) mapper that induces desired distribution of "one" in a codeword. The third contribution considers two-way relay channels where the information exchange between two nodes takes place in two transmission phases using a coding scheme called physical-layer network coding. At the relay, a near optimal decoding strategy is derived using a list decoding algorithm, and an approximation is obtained by a joint decoding approach. For the latter scheme, an analytical approximation of the word error rate based on a union bounding technique is computed under the assumption that linear codes are employed at the two nodes exchanging data. Further, when the wireless channel is frequency selective, two decoding strategies at the relay are developed, namely, a near optimal decoding scheme implemented using list decoding, and a reduced complexity detection/decoding scheme utilizing a linear minimum mean squared error based detector followed by a network coded sequence decoder.

There is a growing interest in the creation of three-dimensional (3D) images and videos due to the growing demand for 3D visual media in commercial markets. A possible solution to produce 3D media files is to convert existing 2D images and videos to 3D. The 2D to 3D conversion methods that estimate the depth map from 2D scenes for 3D reconstruction present an efficient approach to save on the cost of the coding, transmission and storage of 3D visual media in practical applications. Various 2D to 3D conversion methods based on depth maps have been developed using existing image and video processing techniques. The depth maps can be estimated either from a single 2D view or from multiple 2D views. This thesis presents a MATLAB-based 2D to 3D conversion system from multiple views based on the computation of a sparse depth map. The 2D to 3D conversion system is able to deal with the multiple views obtained from uncalibrated hand-held cameras without knowledge of the prior camera parameters or scene geometry. The implemented system consists of techniques for image feature detection and registration, two-view geometry estimation, projective 3D scene reconstruction and metric upgrade to reconstruct the 3D structures by means of a metric transformation. The implemented 2D to 3D conversion system is tested using different multi-view image sets. The obtained experimental results of reconstructed sparse depth maps of feature points in 3D scenes provide relative depth information of the objects. Sample ground-truth depth data points are used to calculate a scale factor in order to estimate the true depth by scaling the obtained relative depth information using the estimated scale factor. It was found out that the obtained reconstructed depth map is consistent with the ground-truth depth data.