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Concept# Washington (state)

Summary

Washington (ˈwɑːʃɪŋtən), officially the State of Washington, is a state in the Pacific Northwest region of the Western United States. Named for George Washington—the first U.S. president—the state was formed from the western part of the Washington Territory, which was ceded by the British Empire in 1846, by the Oregon Treaty in the settlement of the Oregon boundary dispute. The state is bordered on the west by the Pacific Ocean, Oregon to the south, Idaho to the east, and the Canadian province of British Columbia to the north. It was admitted to the Union as the 42nd state in 1889. Olympia is the state capital; the state's largest city is Seattle.
Washington is the 18th-largest state, with an area of , and the 13th-most populous state, with more than 7.7 million people. The majority of Washington's residents live in the Seattle metropolitan area, the center of transportation, business, and industry on Puget Sound, an inlet of the Pacific Ocean consisting of numerous i

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The main goal in network information theory is to identify fundamental limits of communication over networks, and design solutions which perform close to such limits. After several decades of effort, many important problems still do not have a characterization of achievable performance in terms of a finite dimensional description. Given this discouraging state of affairs, a natural question to ask is whether there are systematic approaches to make progress on these open questions. Recently, there has been significant progress on several open questions by seeking a (provably) approximate characterization for these open questions. The main goal of approximation in network information theory is to obtain a universal approximation gap between the achievable and the optimal performance. This approach consists of four ingredients: simplify the model, obtain optimal solution for the simplified model, translate this optimal scheme and outer bounds back to the original model, and finally bound the gap between what can be achieved using the obtained technique and the outer bound. Using such an approach, recent progress has been made in several problems such as the Gaussian interference channel, Gaussian relay networks, etc. In this thesis, we demonstrate that this approach is not only successful in problems of transmission over noisy networks, but gives the first approximation for a network data compression problem. We use this methodology to (approximately) resolve problems that have been open for several decades. Not only do we give theoretical characterization, but we also develop new coding schemes that are required to satisfy this approximate optimality property. These ideas could give insights into efficient design of future network communication systems. This thesis is split into two main parts. The first part deals with the approximation in lossy network data compression. Here, a lossy data compression problem is approximated by a lossless counterpart problem, where all the bits in the binary expansion of the source above the required distortion have to be losslessly delivered to the destination. In particular, we study the multiple description (MD) problem, based on the multi-level diversity (MLD) coding problem. The symmetric version of the MLD problem is well-studied, and we can directly use it to approximate the symmetric MD problem. We formulate the asymmetric multi-level diversity problem, and solve it for three-description case. The optimal solution for this problem, which will be later used to approximate the asymmetric multiple description problem, is based on jointly compressing of independent sources. In both symmetric and asymmetric cases, we derive inner and outer bounds for the achievable rate region, which together with the gap analysis, provide an approximate solution for the problem. In particular, we resolve the symmetric Gaussian MD problem, which has been open for three decades, to within 1 bit. In the second part, we initiate a study of a Gaussian relay-interference network, in which relay (helper) nodes are to facilitate competing information flows over a wireless network. We focus on a two-stage relay-interference network where there are weak cross-links, causing the networks to behave like a chain of Z Gaussian channels. For these Gaussian ZZ and ZS networks, we establish an approximate characterization of the rate region. The outer bounds to the capacity region are established using genie-aided techniques that yield bounds sharper than the traditional cut-set outer bounds. For the inner bound of the ZZ network, we propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This technique allows for over-the-air interference removal, without the transmitters having complete access to the interfering signals. We use insights gained from an exact characterization of the corresponding linear deterministic version of the problem, in order to study the Gaussian network. We resolve the Gaussian relay-interference network to within 2 bits. The new interference management technique (interference neutralization) shows the use of structured lattice codes in the problem. We also consider communication from a source to a destination over a wireless network with the help of a set of authenticated relays, and presence of an adversarial jammer who wishes to disturb communication. We focus on a special diamond network, and show that use of interference suppression (nulling) is crucial to approach the capacity of the network. The exact capacity characterization for the deterministic network, along with an approximate characterization (to within 4 bits) for the Gaussian network is provided. The common theme that binds the diverse network communication problems in this thesis is that of approximate characterization, when exact resolutions are difficult. The approach of focusing on the deterministic/lossless problems underlying the noisy/lossy network communication problems has allowed us to develop new techniques to study these questions. These new techniques might be of independent interest in other network information theory problems.

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Seattle

Seattle (siˈætəl ) is a seaport city on the West Coast of the United States. It is the seat of King County, Washington. With a 2022 population of 749,256 it is the most populous city in both the state

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The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America and consisting of 50 states, a federal distr

Pacific Northwest

The Pacific Northwest (PNW), sometimes referred to as Cascadia, is a geographic region in western North America bounded by its coastal waters of the Pacific Ocean to the west and, loosely, by the Ro