This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

Information Theory and Reliable Communication

Sphere Packings, Lattices and Groups

Systems and methods for implementing array cameras configured to perform super- resolution processing to generate higher resolution super-resolved images using a plurality of captured images and lens stack arrays that can be utilized in array cameras are disclosed. Lens stack arrays in accordance with many embodiments of the invention include lens elements formed on substrates separated by spacers, where the lens elements, substrates and spacers are configured to form a plurality of optical channels, at least one aperture located within each optical channel, at least one spectral filter located within each optical channel, where each spectral filter is configured to pass a specific spectral band of light, and light blocking materials located within the lens stack array to optically isolate the optical channels.

Capturing and processing of images using monolithic camera array with heterogeneous imagers

Product design is a highly involved, often ill-defined, complex and iterative process, and the needs and specifications of the required artifact get more refined only as the design process moves toward its goal. An effective computer support tool that helps the designer make better-informed decisions requires efficient knowledge representation schemes. In today's world, there is a virtual explosion in the amount of raw data available to the designer, and knowledge representation is critical in order to sift through this data and make sense of it. In addition, the need to stay competitive has shrunk product development time through the use of simultaneous and collaborative design processes, which depend on effective transfer of knowledge between teams. Finally, the awareness that decisions made early in the design process have a higher impact in terms of energy, cost, and sustainability, has resulted in the need to project knowledge typically required in the later stages of design to the earlier stages. Research in design rationale systems, product families, systems engineering, and ontology engineering has sought to capture knowledge from earlier product design decisions, from the breakdown of product functions and associated physical features, and from customer requirements and feedback reports. VR (Virtual reality) systems and multidisciplinary modeling have enabled the simulation of scenarios in the manufacture, assembly, and use of the product. This has helped capture vital knowledge from these stages of the product life and use it in design validation and testing. While there have been considerable and significant developments in knowledge capture and representation in product design, it is useful to sometimes review our position in the area, study the evolution of research in product design, and from past and current trends, try and foresee future developments. The goal of this paper is thus to review both our understanding of the field and the support tools that exist for the purpose, and identify the trends and possible directions research can evolve in the future.

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The evolution, challenges, and future of knowledge representation in product design systems

Caching is a technique to reduce the communication load in peak hours by prefetching contents during off-peak hours. Recently Maddah-Ali and Niesen introduced an information theoretic framework for coded caching, and showed that significant improvement can be obtained compared to uncoded caching. Considerable efforts have been devoted to identify the precise information theoretic fundamental limit of such systems, however the difficulty of this task has also become clear. One of the reasons for this difficulty is that the original coded caching setting allows multiple demand types during delivery, which in fact introduces tension in the coding strategy to accommodate all of them. In this paper, we seek to develop a better understanding of the fundamental limit of coded caching by investigating single demand type systems. We first show that in the canonical three-user three-file systems, such single demand type systems already provide important insights. Motivated by these findings, we focus on systems where the number of users and the number of files are the same, and the demand type is when all files are being requested. A novel coding scheme is proposed, which provides several optimal memory-transmission operating points. Outer bounds for this class of systems are also considered, and their relation with existing bounds is discussed.

On the Fundamental Limit of Coded Caching Systems with a Single Demand Type

In the conventional robust $T$ -colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any $T$ colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the ( $N, T_{1}: K_{1}, T_{2}: K_{2}$ ) two-level PIR system, where $K_{1}$ messages need to be retrieved privately against $T_{1}$ colluding servers, and all the messages need to be retrieved privately against $T_{2}$ colluding servers where $T_{2}\leq T_{1}$ . We obtain a lower bound to the capacity by proposing a novel coding scheme, namely the non-uniform successive cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bound is analyzed, and shown to vanish when $T_{1}=T_{2}$ .

Two-Level Private Information Retrieval

It is well-known that optimal digital coding schemes based on the source-channel separation principle suffer from the ``threshold effect" that they are sensitive to the channel condition. If the channel condition is worse than what the code is designed for, the code will fail to decode completely; on the other hand, if the channel condition is in fact better, a digital code can not provide any performance improvement. There exist more robust joint source-channel coding schemes in the literature which can achieve optimal performance for a given channel condition, and at the same time, either being useful when the channel condition is worse, or offering performance improvement when the channel condition is better, but not both. In this paper, we propose several schemes which use hybrid analog and digital signaling to provide benefits in both cases {\em simultaneously}, while still keeping it optimal for a given target channel condition. We further show that compared to the best known optimal schemes designed for the target channel condition, which takes into account only the worse channel condition, or only the better channel condition, these new set of schemes can in fact achieve the same performances for the better and the worse channel conditions simultaneously.

Sending Gaussian Source on Bandwidth-Mismatched Gaussian Channel with Improved Robustness

We consider the $(n,k,d,\ell)$ secure exact-repair regenerating code problem, which generalizes the $(n,k,d)$ exact-repair regenerating code problem with the additional constraint that the stored file needs to be kept information-theoretically secure against an eavesdropper, who can access the data transmitted to regenerate a total of $\ell$ different failed nodes. For all known results on this problem, the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints are known to have multiple corner points in general, these existing results suggest a phase-change-like behavior, i.e., enforcing a secrecy constraint ($\ell\geq 1$) immediately reduces the tradeoff region to one with a single corner point. In this work, we first show that when the secrecy parameter $\ell$ is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when $\ell$ is small, we show that the tradeoff region can in fact have multiple corner points. In particular, we establish a precise characterization of the tradeoff region for the $(7,6,6,1)$ problem, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened.

On the Tradeoff Region of Secure Exact-Repair Regenerating Codes

We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The two scenarios for which separation is optimal complement each other: the first is when the memoryless sources at source nodes are arbitrarily correlated, each of which is to be reconstructed at possibly multiple destinations within certain distortions, but the channels in this network are synchronized, orthogonal and memoryless point-to-point channels; the second is when the memoryless sources are mutually independent, each of which is to be reconstructed only at one destination within a certain distortion, but the channels are general, including multi-user channels such as multiple access, broadcast, interference and relay channels, possibly with feedback. The third scenario, for which we demonstrate approximate optimality of source-channel separation, generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions. For this case, the loss from optimality by using the separation approach can be upper-bounded when a "difference" distortion measure is taken, and in the special case of quadratic distortion measure, this leads to universal constant bounds.

Chao Tian

Papers

On the Fundamental Limit of Coded Caching Systems with a Single Demand Type

Two-Level Private Information Retrieval

Sending Gaussian Source on Bandwidth-Mismatched Gaussian Channel with Improved Robustness

On the Tradeoff Region of Secure Exact-Repair Regenerating Codes

Optimality and Approximate Optimality of Source-Channel Separation in Networks