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Publication# Lossy Network Correlated Data Gathering with High-Resolution Coding

Résumé

Sensor networks measuring correlated data are considered, where the task is to gather data from the network nodes to a sink. A specific scenario is addressed, where data at nodes are lossy coded with high-resolution, and the information measured by the nodes has to be reconstructed at the sink within both certain total and individual distortion bounds. The first problem considered is to find the optimal transmission structure and the rate-distortion allocations at the various spatially located nodes, such as to minimize the total power consumption cost of the network, by assuming fixed nodes positions. The optimal transmission structure is the shortest path tree and the problems of rate and distortion allocation separate in the high-resolution case, namely, first the distortion allocation is found as a function of the transmission structure, and second, for a given distortion allocation, the rate allocation is computed. The second problem addressed is the case when the node positions can be chosen, by finding the optimal node placement for two different targets of interest, namely total power minimization and network lifetime maximization. Finally, a node placement solution that provides a tradeoff between the two metrics is proposed.

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Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal number of bits

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Razvan Cristescu, Martin Vetterli

We consider the problem of correlated data gathering by a network with a sink node and a tree based communication structure, where the goal is to minimize the total trans- mission cost of transporting the information collected by the nodes, to the sink node. For source coding of correlated data, we consider a joint entropy based coding model with explicit communication where coding is simple and the transmission structure optimiza- tion is difficult. We first formulate the optimization problem definition in the general case and then we study further a network setting where the entropy conditioning at nodes does not depend on the amount of side information, but only on its availability. We prove that even in this simple case, the optimization problem is NP-hard. We propose some efficient, scalable, and distributed heuristic approximation algorithms for solving this problem and show by numerical simulations that the total transmission cost can be significantly improved over direct transmission or the shortest path tree. We also present an approximation algorithm that provides a tree transmission structure with total cost within a constant factor from the optimal.

2006We live in a world characterized by massive information transfer and real-time communication. The demand for efficient yet low-complexity algorithms is widespread across different fields, including machine learning, signal processing and communications. Most of the problems that we encounter across these disciplines involves a large number of modules interacting with each other. It is therefore natural to represent these interactions and the flow of information between the modules in terms of a graph. This leads to the study of graph-based information processing framework. This framework can be used to gain insight into the development of algorithms for a diverse set of applications. We investigate the behaviour of large-scale networks (ranging from wireless sensor networks to social networks) as a function of underlying parameters. In particular, we study the scaling laws and applications of graph-based information processing in sensor networks/arrays, sparsity pattern recovery and interactive content search. In the first part of this thesis, we explore location estimation from incomplete information, a problem that arises often in wireless sensor networks and ultrasound tomography devices. In such applications, the data gathered by the sensors is only useful if we can pinpoint their positions with reasonable accuracy. This problem is particularly challenging when we need to infer the positions based on basic information/interaction such as proximity or incomplete (and often noisy) pairwise distances. As the sensors deployed in a sensor network are often of low quality and unreliable, we need to devise a mechanism to single out those that do not work properly. In the second part, we frame the network tomography problem as a well-studied inverse problem in statistics, called group testing. Group testing involves detecting a small set of defective items in a large population by grouping a subset of items into different pools. The result of each pool is a binary output depending on whether the pool contains a defective item or not. Motivated by the network tomography application, we consider the general framework of group testing with graph constraints. As opposed to conventional group testing where any subset of items can be grouped, here a test is admissible if it induces a connected subgraph. Given this constraint, we are interested in bounding the number of pools required to identify the defective items. Once the positions of sensors are known and the defective sensors are identified, we investigate another important feature of networks, namely, navigability or how fast nodes can deliver a message from one end to another by means of local operations. In the final part, we consider navigating through a database of objects utilizing comparisons. Contrary to traditional databases, users do not submit queries that are subsequently matched to objects. Instead, at each step, the database presents two objects to the user, who then selects among the pair the object closest to the target that she has in mind. This process continues until, based on the user’s answers, the database can identify the target she has in mind. The search through comparisons amounts to determining which pairs should be presented to the user in order to find the target object as quickly as possible. Interestingly, this problem has a natural connection with the navigability property studied in the second part, which enables us to develop efficient algorithms.

The celebrated distributed computing approach for building systems and services using multiple machines continues to expand to new domains. Computation devices nowadays have additional sensing and communication capabilities, while becoming, at the same time, cheaper, faster and more pervasive. Consequently, areas like industrial control, smart grids and sensor networks are increasingly using such devices to control and coordinate system operations. However, compared to classic distributed systems, such real-world physical systems have different needs, e.g., real-time and energy efficiency requirements. Moreover, constraints that govern communication are also different. Networks become susceptible to inevitable random losses, especially when utilizing wireless and power line communication. This thesis investigates how to build various fundamental distributed computing abstractions (services) given the limitations, the performance and the application requirements and constraints of real-world control, smart grid and sensor systems. In quest of completeness, we discuss four distributed abstractions starting from the level of network links all the way up to the application level. At the link level, we show how to build an energy-efficient reliable communication service. This is especially important for devices with battery-powered wireless adapters where recharging might be unfeasible. We establish transmission policies that can be used by processes to decide when to transmit over the network in order to avoid losses and minimize re-transmissions. These policies allow messages to be reliably transmitted with minimum transmission energy. One level higher than links is failure detection, a software abstraction that relies on communication for identifying process crashes. We prove impossibility results concerning implementing classic eventual failure detectors in networks with probabilistic losses. We define a new implementable type of failure detectors, which preserves modularity. This means that existing deterministic algorithms using eventual failure detectors can still be used to solve certain distributed problems in lossy networks: we simply replace the existing failure detector with the one we define. Using failure detectors, processes might get information about failures at different times. However, to ensure dependability, environments such as distributed control systems (DCSs), require a membership service where processes agree about failures in real time. We prove that the necessary properties of this membership cannot be implemented deterministically, given probabilistic losses. We propose an algorithm that satisfies these properties, with high probability. We show analytically, as well as experimentally (within an industrial DCS), that our technique significantly enhances the DCS dependability, compared to classic membership services, at low additional cost. Finally, we investigate a real-time shared memory abstraction, which vastly simplifies programming control applications. We study the feasibility of implementing such an abstraction within DCSs, showing the impossibility of this task using traditional algorithms that are built on top of existing software blocks like failure detectors. We propose an approach that circumvents this impossibility by attaching information to the failure detection messages, analyze the performance of our technique and showcase ways of adapting it to various application needs and workloads.