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

This paper considers the transmission of confidential data over wireless channels. Based on an information-theoretic formulation of the problem, in which two legitimates partners communicate over a quasi-static fading channel and an eavesdropper observes their transmissions through a second independent quasi-static fading channel, the important role of fading is characterized in terms of average secure communication rates and outage probability. Based on the insights from this analysis, a practical secure communication protocol is developed, which uses a four-step procedure to ensure wireless information-theoretic security: (i) common randomness via opportunistic transmission, (ii) message reconciliation, (iii) common key generation via privacy amplification, and (iv) message protection with a secret key. A reconciliation procedure based on multilevel coding and optimized low-density parity-check (LDPC) codes is introduced, which allows to achieve communication rates close to the fundamental security limits in several relevant instances. Finally, a set of metrics for assessing average secure key generation rates is established, and it is shown that the protocol is effective in secure key renewal-even in the presence of imperfect channel state information.

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Wireless Information-Theoretic Security

Sphere Packings, Lattices and Groups

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

High-resolution oxygen isotope records document the timing and magnitude of global warming across the Permian-Triassic (P-Tr) boundary. Oxygen isotope ratios measured on phosphate-bound oxygen in conodont apatite from the Meishan and Shangsi sections (South China) decrease by 2‰ in the latest Permian, translating into low-latitude surface water warming of 8 °C. The oxygen isotope shift coincides with the negative shift in carbon isotope ratios of carbonates, suggesting that the addition of isotopically light carbon to the ocean-atmosphere system by Siberian Traps volcanism and related processes resulted in higher greenhouse gas levels and global warming. The major temperature rise started immediately before the main extinction phase, with maximum and harmful temperatures documented in the latest Permian (Meishan: bed 27). The coincidence of climate warming and the main pulse of extinction suggest that global warming was one of the causes of the collapse of the marine and terrestrial ecosystems. In addition, very warm climate conditions in the Early Triassic may have played a major role in the delayed recovery in the aftermath of the Permian-Triassic crisis.

Climate warming in the latest Permian and the Permian-Triassic mass extinction

We propose an end-to-end trainable Convolutional Neural Network (CNN), named GridDehazeNet, for single image dehazing. The GridDehazeNet consists of three modules: pre-processing, backbone, and post-processing. The trainable pre-processing module can generate learned inputs with better diversity and more pertinent features as compared to those derived inputs produced by hand-selected pre-processing methods. The backbone module implements a novel attention-based multi-scale estimation on a grid network, which can effectively alleviate the bottleneck issue often encountered in the conventional multi-scale approach. The post-processing module helps to reduce the artifacts in the final output. Experimental results indicate that the GridDehazeNet outperforms the state-of-the-arts on both synthetic and real-world images. The proposed hazing method does not rely on the atmosphere scattering model, and we provide an explanation as to why it is not necessarily beneficial to take advantage of the dimension reduction offered by the atmosphere scattering model for image dehazing, even if only the dehazing results on synthetic images are concerned.

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GridDehazeNet: Attention-Based Multi-Scale Network for Image Dehazing

We consider a distributed sensor network in which several observations are communicated to the fusion center using limited transmission rate. The observation must be separately encoded so that the target can be estimated with minimum average distortion. We address the problem from an information theoretic perspective and establish the inner and outer bound of the admissible rate-distortion region. We derive an upper bound on the sum-rate distortion function and its corresponding rate allocation schemes by exploiting the contra-polymatroid structure of the achievable rate region. The quadratic Gaussian case is analyzed in detail and the optimal rate allocation schemes in the achievable rate region are characterized. We show that our upper bound on the sum-rate distortion function is tight for the quadratic Gaussian CEO problem in the case of same signal-to-noise ratios at the sensors.

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An upper bound on the sum-rate distortion function and its corresponding rate allocation schemes for the CEO problem

We consider a class of finite-state Markov channels with feedback. We first introduce a simplified equivalent channel model, and then construct the optimal stationary and nonstationary input processes that maximize the long-term directed mutual information. Furthermore, we give a sufficient condition under which the channel's Shannon capacity can be achieved by a stationary input process. The corresponding converse coding theorem and direct coding theorem are proved.

The capacity of finite-State Markov Channels With feedback

C record of carbonate rocks (δ 13 C carb ), for the selective extinction of heavily calcifi ed marine animals, and for the abrupt transition in carbonate facies across the extinction horizon, an additional proxy is necessary to distinguish among these options. Calcium isotopes hold promise for differentiating between suggested scenarios for change in seawater carbonate chemistry linked with the end-Permian extinction. The calcium cycle is linked to the carbon cycle through the weathering of limestone and the deposition of calcium carbonate sediments. Calcium isotopes fractionate by ~0.6‰ and ~1.3‰ in calcite and aragonite, respectively, during the precipitation of modern carbonate minerals, meaning carbonate sediments are enriched in the lighter isotope relative to the seawater from which they precipitated (Skulan et al., 1997; Tang et al., 2008). Imbalances between calcium delivery and burial fl uxes and changes in the magnitude of fractionation during carbonate deposition will result in changes in the δ 44/40 Ca of seawater and will be recorded in marine sediments (DePaolo, 2004; Farkao et al., 2007). Therefore, variation in the δ

Jun Chen

Papers

Climate warming in the latest Permian and the Permian-Triassic mass extinction

GridDehazeNet: Attention-Based Multi-Scale Network for Image Dehazing

An upper bound on the sum-rate distortion function and its corresponding rate allocation schemes for the CEO problem

The capacity of finite-State Markov Channels With feedback

Evidence for end-Permian ocean acidification from calcium isotopes in biogenic apatite