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.

/pdf/the-evolution-challenges-and-future-of-knowledge-2l8tzvf3b5.pdf

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

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

We address the issue of safety in reinforcement learning. We pose the problem in a discounted infinite-horizon constrained Markov decision process framework. Existing results have shown that gradient-based methods are able to achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate both for the optimality gap and the constraint violation. We exhibit a natural policy gradient-based algorithm that has a faster convergence rate $\mathcal{O}(\log(T)/T)$ for both the optimality gap and the constraint violation. When Slater's condition is satisfied and known a priori, zero constraint violation can be further guaranteed for a sufficiently large $T$ while maintaining the same convergence rate.

Fast Global Convergence of Policy Optimization for Constrained MDPs.

The problem of simultaneous message transmission and state amplification in a Gaussian channel with additive Gaussian state is studied when the sender has imperfect noncausal knowledge of the state sequence. Inner and outer bounds to the rate--state-distortion region are provided. The coding scheme underlying the inner bound combines analog signaling and Gelfand-Pinsker coding, where the latter deviates from the operating point of Costa's dirty paper coding.

Gaussian State Amplification with Noisy State Observations

We developed an open-source C library of repair-efficient erasure codes for distributed data storage systems, which includes five classes of such codes in the literature. Because of the more involved coding structures of these codes, they are more suitable to be viewed as array codes. From this perspective, all these codes can have a uniform encoding and decoding interface. We also discuss the basic principles of the data arrangement, choice of algorithms, and then evaluate the coding speed of these encoding and decoding functions.

A C library of repair-efficient erasure codes for distributed data storage systems

Decentralized coded caching is applicable in scenarios where the server does not have enough knowledge about the entire cache network to perform centralized coordination during prefetching, such as when the server is uninformed of the number of active users and their identities in a wireless or mobile environment. Most of known decentralized strategies use random uncoded prefetching followed by coded delivery, which is partly motivated by the simplicity but also partly motivated by the existing centralized coding strategy which has such properties. Recent results have shown that in the centralized setting, coded prefetching can provide performance improvement in some cases when the numbers of files is less than the number of users, and particularly, non-binary codes can be beneficial. This naturally raises the questions whether the corresponding decentralized counterpart using non-binary codes can also provide improvement, and what is the necessary overhead to accomplish such decentralization. In this work we propose a decentralized coded prefetching strategy where both prefetching and delivery are coded. The proposed strategy indeed outperforms the existing decentralized uncoded caching strategy in regimes of small cache size M when the numbers of files is less than the number of users. Methods to manage the coding overhead are further suggested.

Chao Tian

Papers

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

Fast Global Convergence of Policy Optimization for Constrained MDPs.

Gaussian State Amplification with Noisy State Observations

A C library of repair-efficient erasure codes for distributed data storage systems

Coded prefetching and efficient delivery in decentralized caching systems