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

We present a novel technique for encoding and decoding constant weight binary vectors that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the vector, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length.

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A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections

In the canonical private information retrieval (PIR) problem, a user retrieves a message from a set of databases without allowing any individual database to obtain any knowledge regarding the identity of the requested message. This perfect privacy requirement may be too stringent in many cases, and the user may only wish to control the amount of the privacy leakage to below a given level, and in return, can retrieve the message at a lower communication cost. In this work, we study the tradeoff between the download cost and the amount of privacy leakage under the maximal leakage metric. A new scheme is proposed by allowing a more flexible query structure and probability distributions in a code previously proposed by Tian et al., which utilized a fixed query set and a uniform distribution. It is shown that the optimal probability distribution in the proposed scheme has a particularly simple structure, which leads to a closed form achievability bound for the optimal tradeoff between the download cost and the privacy leakage. The proposed scheme includes several known schemes, such as those proposed by Lin et al., by Samy et al., and by Jia, as special cases.

Weakly Private Information Retrieval Under the Maximal Leakage Metric

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 paper, 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

Digital contents distributed storage systems may have different reliability and access delay requirements, and erasure codes with different strengths can provide the best storage efficiency in these systems. At the same time, in such large-scale distributed storage systems, nodes fail on a regular basis, and the contents stored on them need to be regenerated from the data downloaded from the remaining nodes. The efficiency of this repair process is an important factor that affects the overall quality of service. In this paper, we formulate the problem of multilevel diversity coding with regeneration to address these considerations, for which the storage versus repair-bandwidth tradeoff is investigated. We show that the extreme point on the optimal tradeoff curve that corresponds to the minimum possible storage can be achieved by a simple coding scheme, in which contents with different reliability requirements are encoded separately with individual regenerating codes without any mixing. On the other hand, we establish the complete storage-repair-bandwidth tradeoff for the case of four storage nodes, which reveals that codes mixing different contents can, in general, strictly improve the optimal tradeoff over the separate-coding solution.

Multilevel Diversity Coding With Regeneration

We provide a complete characterization of the achievable distortion region for the problem of sending a bivariate Gaussian source over a bandwidth-matched Gaussian broadcast channel, where each receiver is interested in only one component of the source. This setting naturally generalizes the simple single Gaussian source bandwidth-matched broadcast problem for which the uncoded scheme is known to be optimal. We show that a hybrid scheme can achieve the optimum for the bivariate case, but neither an uncoded scheme alone nor a separation-based scheme alone is sufficient.

Chao Tian

Papers

A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections

Weakly Private Information Retrieval Under the Maximal Leakage Metric

On the Tradeoff Region of Secure Exact-Repair Regenerating Codes

Multilevel Diversity Coding With Regeneration

The achievable distortion region of bivariate Gaussian source on Gaussian broadcast channel