Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity

Side information aware source and channel coding in wireless networks

Signals in communication networks exhibit significant correlation, which can stem from the physical nature of the underlying sources, or can be created within the system. Current layered network architectures, in which, based on Shannon’s separation theorem, data is compressed and transmitted over independent bit-pipes, are in general not able to exploit such correlation efficiently. Moreover, this strictly layered architecture was developed for wired networks and ignore the broadcast and highly dynamic nature of the wireless medium, creating a bottleneck in the wireless network design. Technologies that exploit correlated information and go beyond the layered network architecture can become a key feature of future wireless networks, as information theory promises significant gains. In this thesis, we study from an information theoretic perspective, three distinct, yet fundamental, problems involving the availability of correlated information in wireless networks and develop novel communication techniques to exploit it efficiently. We first look at two joint source-channel coding problems involving the lossy transmission of Gaussian sources in a multi-terminal and a time-varying setting in which correlated side information is present in the network. In these two problems, the optimality of Shannon’s separation breaks down and separate source and channel coding is shown to perform poorly compared to the proposed joint source-channel coding designs, which are shown to achieve the optimal performance in some setups. Then, we characterize the capacity of a class of orthogonal relay channels in the presence of channel side information at the destination, and show that joint decoding and compression of the received signal at the relay is required to optimally exploit the available side information. Our results in these three different scenarios emphasize the benefits of exploiting correlated side information at the destination when designing a communication system, even though the nature of the side information and the performance measure in the three scenarios are quite different.Open Acces

A Unified Approach for Network Information Theory

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter expression has a very simple form, which was made possible by many novel elements such as a unified framework that represents various network problems in a simple and unified way, a unified coding strategy that consists of a few basic ingredients but can emulate many known coding techniques if needed, and new proof techniques beyond the use of standard covering and packing lemmas. For example, in our framework, sources, channels, states and side information are treated in a unified way and various constraints such as cost and distortion constraints are unified as a single joint-typicality constraint. Our theorem can be useful in proving many new achievability results easily and in some cases gives simpler rate expressions than those obtained using conventional approaches. Furthermore, our unified coding can strictly outperform existing schemes. For example, we obtain a generalized decode-compress-amplify-and-forward bound as a simple corollary of our main theorem and show it strictly outperforms previously known coding schemes. Using our unified framework, we formally define and characterize three types of network duality based on channel input-output reversal and network flow reversal combined with packing-covering duality.Comment: 52 pages, 7 figures, submitted to IEEE Transactions on Information theory, a shorter version will appear in Proc. IEEE ISIT 201

Lecture Notes on Network Information Theory

These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Coding for Relay Networks with Parallel Gaussian Channels

A wireless relay network consists of multiple source nodes, multiple destination nodes, and possibly many relay nodes in between to facilitate its transmission. It is clear that the performance of such networks highly depends on information for- warding strategies adopted at the relay nodes. This dissertation studies a particular information forwarding strategy called compute-and-forward. Compute-and-forward is a novel paradigm that tries to incorporate the idea of network coding within the physical layer and hence is often referred to as physical layer network coding. The main idea is to exploit the superposition nature of the wireless medium to directly compute or decode functions of transmitted signals at intermediate relays in a net- work. Thus, the coding performed at the physical layer serves the purpose of error correction as well as permits recovery of functions of transmitted signals. For the bidirectional relaying problem with Gaussian channels, it has been shown by Wilson et al. and Nam et al. that the compute-and-forward paradigm is asymptotically optimal and achieves the capacity region to within 1 bit; however, similar results beyond the memoryless case are still lacking. This is mainly because channels with memory would destroy the lattice structure that is most crucial for the compute-and-forward paradigm. Hence, how to extend compute-and-forward to such channels has been a challenging issue. This motivates this study of the extension of compute-and-forward to channels with memory, such as inter-symbol interference. The bidirectional relaying problem with parallel Gaussian channels is also studied, which is a relevant model for the Gaussian bidirectional channel with inter-symbol interference and that with multiple-input multiple-output channels. Motivated by the recent success of linear finite-field deterministic model, we first investigate the corresponding deterministic parallel bidirectional relay channel and fully characterize its capacity region. Two compute-and-forward schemes are then proposed for the Gaussian model and the capacity region is approximately characterized to within a constant gap. The design of coding schemes for the compute-and-forward paradigm with low decoding complexity is then considered. Based on the separation-based framework proposed previously by Tunali et al., this study proposes a family of constellations that are suitable for the compute-and-forward paradigm. Moreover, by using Chinese remainder theorem, it is shown that the proposed constellations are isomorphic to product fields and therefore can be put into a multilevel coding framework. This study then proposes multilevel coding for the proposed constellations and uses multistage decoding to further reduce decoding complexity

Physical-Layer Security in Wireless Communication Systems

The use of wireless networks has grown significantly in contemporary times, and continues to develop further. The broadcast nature of wireless communications, however, makes them particularly vulnerable to eavesdropping. Unlike traditional solutions, which usually handle security at the application layer, the primary concern of this dissertation is to analyze and develop solutions based on coding techniques at the physical-layer. First, in chapter $2$, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper, and present an inner bound on the secrecy capacity region for this model. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. We further study the situation in which the channels are degraded. For the degraded broadcast channel with an eavesdropper, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as the Secret Superposition Scheme. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise and show that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costa's entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdropper's channel is fixed and known at the transmitter. We derive the optimum power allocation for the coding layers, which maximizes the total average rate. Second, in chapter $3$ , we consider the Multiple-Input-Multiple-Output (MIMO) scenario of a broadcast channel where a wiretapper also receives the transmitted signal via another MIMO channel. First, we assume that the channels are degraded and the wiretapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is the Secret Superposition Coding. For the outerbound, we use notion of the enhanced channels to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. We then extend the result of the degraded case to a non-degraded case. We show that the secret superposition of Gaussian codes, along with successive decoding, cannot work when the channels are not degraded. We develop a Secret Dirty Paper Coding scheme and show that it is optimal for this channel. We then present a corollary generalizing the capacity region of the two receivers case to the case of multiple receivers. Finally, we investigate a scenario which frequently occurs in the practice of wireless networks. In this scenario, the transmitter and the eavesdropper have multiple antennae, while both intended receivers have a single antenna (representing resource limited mobile units). We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers' channels and the eavesdropper's channel. We refer to this configuration as the MISOME case. We then present a corollary generalizing the results of the two receivers case to multiple receivers. In the high SNR regime, we show that the capacity region is a convex closure of rectangular regions. Finally, in chapter $4$, we consider a $K$-user secure Gaussian Multiple-Access-Channel with an external eavesdropper. We establish an achievable rate region for the secure discrete memoryless MAC. Thereafter, we prove the secrecy sum capacity of the degraded Gaussian MIMO MAC using Gaussian codebooks. For the non-degraded Gaussian MIMO MAC, we propose an algorithm inspired by the interference alignment technique to achieve the largest possible total Secure-Degrees-of-Freedom . When all the terminals are equipped with a single antenna, Gaussian codebooks have shown to be inefficient in providing a positive S-DoF. Instead, we propose a novel secure coding scheme to achieve a positive S-DoF in the single antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. We use tools from the field of Diophantine Approximation in number theory to analyze the probability of error in the coding scheme. We prove that the total S-DoF of $\frac{K-1}{K}$ can be achieved for almost all channel gains. For the other channel gains, we propose a multi-layer coding scheme to achieve a positive S-DoF. As a function of channel gains, therefore, the achievable S-DoF is discontinued

Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications

Communication systems to date primarily aim at reliably communicating bit sequences. Such an approach provides efficient engineering designs that are agnostic to the meanings of the messages or to the goal that the message exchange aims to achieve. Next generation systems, however, can be potentially enriched by folding message semantics and goals of communication into their design. Further, these systems can be made cognizant of the context in which communication exchange takes place, providing avenues for novel design insights. This tutorial summarizes the efforts to date, starting from its early adaptations, semantic-aware and task-oriented communications, covering the foundations, algorithms and potential implementations. The focus is on approaches that utilize information theory to provide the foundations, as well as the significant role of learning in semantics and task-aware communications.Comment: 28 pages, 14 figure

Exposing a waveform interface to the wireless channel for scalable video broadcast

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-167).Video broadcast and mobile video challenge the conventional wireless design. In broadcast and mobile scenarios the bit-rate supported by the channel differs across receivers and varies quickly over time. The conventional design however forces the source to pick a single bit-rate and degrades sharply when the channel cannot support it. This thesis presents SoftCast, a clean-slate design for wireless video where the source transmits one video stream that each receiver decodes to a video quality commensurate with its specific instantaneous channel quality. To do so, SoftCast ensures the samples of the digital video signal transmitted on the channel are linearly related to the pixels' luminance. Thus, when channel noise perturbs the transmitted signal samples, the perturbation naturally translates into approximation in the original video pixels. Hence, a receiver with a good channel (low noise) obtains a high fidelity video, and a receiver with a bad channel (high noise) obtains a low fidelity video. SoftCast's linear design in essence resembles the traditional analog approach to communication, which was abandoned in most major communication systems, as it does not enjoy the theoretical opimality of the digital separate design in point-topoint channels nor its effectiveness at compressing the source data. In this thesis, I show that in combination with decorrelating transforms common to modern digital video compression, the analog approach can achieve performance competitive with the prevalent digital design for a wide variety of practical point-to-point scenarios, and outperforms it in the broadcast and mobile scenarios. Since the conventional bit-pipe interface of the wireless physical layer (PHY) forces the separation of source and channel coding, to realize SoftCast, architectural changes to the wireless PHY are necessary. This thesis discusses the design of RawPHY, a reorganization of the PHY which exposes a waveform interface to the channel while shielding the designers of the higher layers from much of the perplexity of the wireless channel. I implement SoftCast and RawPHY using the GNURadio software and the USRP platform. Results from a 20-node testbed show that SoftCast improves the average video quality (i.e., PSNR) across diverse broadcast receivers in our testbed by up to 5.5 dB in comparison to conventional single- or multi-layer video. Even for a single receiver, it eliminates video glitches caused by mobility and increases robustness to packet loss by an order of magnitude.by Szymon Kazimierz Jakubczak.Ph.D

Beyond Transmitting Bits: Context, Semantics, and Task-Oriented Communications

Communication systems to date primarily aim at reliably communicating bit sequences. Such an approach provides efficient engineering designs that are agnostic to the meanings of the messages or to the goal that the message exchange aims to achieve. Next generation systems, however, can be potentially enriched by folding message semantics and goals of communication into their design. Further, these systems can be made cognizant of the context in which communication exchange takes place, thereby providing avenues for novel design insights. This tutorial summarizes the efforts to date, starting from its early adaptations, semantic-aware and task-oriented communications, covering the foundations, algorithms and potential implementations. The focus is on approaches that utilize information theory to provide the foundations, as well as the significant role of learning in semantics and task-aware communications