A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the L-infinity norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems.

Rate allocation and optimized decoding in inter-session network coding

Eirina Bourtsoulatze

Recent advances in data processing and communication systems have led to a continuous increase in the amount of data communicated over today’s networks. These large volumes of data pose new challenges on the current networking infrastructure that only offers a best effort mechanism for data delivery. The emergence of new distributed network architectures, such as peer-to-peer networks and wireless mesh networks, and the need for efficient data delivery mechanisms have motivated researchers to reconsider the way that information is communicated and processed in the networks. This has given rise to a new research field called network coding. The network coding paradigm departs from the traditional routing principle where information is simply relayed by the network nodes towards the destination, and introduces some intelligence in the network through coding at the intermediate nodes. This in-network data processing has been proved to substantially improve the performance of data delivery systems in terms of throughput and error resilience in networks with high path diversity. Motivated by the promising results in the network coding research, we focus in this thesis on the design of network coding algorithms for simultaneous transmission of multiple data sources in overlay networks. We investigate several problems that arise in the context of inter-session network coding, namely (i) decoding delay minimization in inter-session network coding, (ii) distributed rate allocation for inter-session network coding and (iii) correlation-aware decoding of incomplete network coded data. We start by proposing a novel framework for data delivery from multiple sources to multiple clients in an overlay wireline network, where intermediate nodes employ randomized inter-session network coding. We consider networks with high resource diversity, which creates network coding opportunities with possibly large gains in terms of throughput, delay and error robustness. However, the coding operations in the intermediate nodes must be carefully designed in order to enable efficient data delivery. We look at the problem from the decoding delay perspective and design solutions that lead to a small decoding delay at clients through proper coding and rate allocation. We cast the optimization problem as a rate allocation problem, which seeks for the coding operations that minimize the average decoding delay in the client population. We demonstrate the validity of our algorithm through simulations in representative network topologies. The results show that an effective combination of intra- and inter-session network coding based on randomized linear coding permits to reach small decoding delays and to better exploit the available network resources even in challenging network settings. Next, we design a distributed rate allocation algorithm where the users decide locally how many intra- and inter-session network coded packets should be requested from the parent nodes in order to get minimal decoding delay. The capability to take coding decisions locally with only a partial knowledge of the network statistics is of crucial importance for applications where users are organized in dynamic overlay networks. We propose a receiver-driven communication protocol that operates in two rounds. First, the users request and obtain information regarding the network conditions and packet availability in their local neighborhood. Then, every user independently optimizes the rate allocation among different possible intra- and inter-session packet combinations to be requested from its parents. We also introduce the novel concept of equivalent flows, which permits to efficiently estimate the expected number of packets that are necessary for decoding and hence to simplify the rate allocation process. Experimental results indicate that our algorithm is capable of eliminating the bottlenecks and reducing the decoding delay of users with limited resources. We further investigate the application of the proposed distributed rate allocation algorithm to the transmission of video sequences and validate the performance of our system using the NS-3 simulator. The simulation results show that the proposed rate allocation algorithm is successful in improving the quality of the delivered video compared to intra-session network coding based solutions. Finally, we investigate the problem of decoding the source information from an incomplete set of network coded data with the help of source priors in a finite algebraic field. The inability to form a complete decoding system can be often caused by transmission losses or timing constraints imposed by the application. In this case, exact reconstruction of the source data by conventional algorithms such as Gaussian elimination is not feasible; however, partial recovery of the source data may still be possible, which can be useful in applications where approximate reconstruction is informative. We use the statistical characteristics of the source data in order to perform approximate decoding. We first analyze the performance of a hypothetical maximum a posteriori decoder, which recovers the source data from an incomplete set of network coded data given the joint statistics of the sources. We derive an upper bound on the probability of erroneous source sequence decoding as a function of the system parameters. We then propose a constructive solution to the approximate decoding problem and design an iterative decoding algorithm based on message passing, which jointly considers the network coding and the correlation constraints. We illustrate the performance of our decoding algorithm through extensive simulations on synthetic and real data sets. The results demonstrate that, even by using a simple correlation model expressed as a correlation noise between pairs of sources, the original source data can be partially decoded in practice from an incomplete set of network coded symbols. Overall, this thesis addresses several important issues related to the design of efficient data delivery methods with inter-session network coding. Our novel framework for decoding delay minimization can impact the development of practical inter-session network coding algorithms that are appropriate for applications with low delay requirements. Our rate allocation algorithms are able to exploit the high resource diversity of modern networking systems and represent an effective alternative in the development of distributed communication systems. Finally, our algorithm for data recovery from incomplete network coded data using correlation priors can contribute significantly to the improvement of the delivered data quality and provide new insights towards the design of joint source and network coding algorithms.

EPFL2013

Interference management in impulse-radio ultra-wide band networks

Ruben Merz

We consider networks of impulse-radio ultra-wide band (IR-UWB) devices. We are interested in the architecture, design, and performance evaluation of these networks in a low data-rate, self-organized, and multi-hop setting. IR-UWB is a potential physical layer for sensor networks and emerging pervasive wireless networks. These networks are likely to have no particular infrastructure, might have nodes embedded in everyday life objects and have a size ranging from a few dozen nodes to large-scale networks composed of hundreds of nodes. Their average data-rate is low, on the order of a few megabits per second. IR-UWB physical layers are attractive for these networks because they potentially combine low-power consumption, robustness to multipath fading and to interference, and location/ranging capability. The features of an IR-UWB physical layer greatly differ from the features of the narrow-band physical layers used in existing wireless networks. First, the bandwidth of an IR-UWB physical layer is at least 500 MHz, which is easily two orders of magnitude larger than the bandwidth used by a typical narrow-band physical layer. Second, this large bandwidth implies stringent radio spectrum regulations because UWB systems might occupy a portion of the spectrum that is already in use. Consequently, UWB systems exhibit extremely low power spectral densities. Finally IR-UWB physical layers offer multi-channel capabilities for multiple and concurrent access to the physical layer. Hence, the architecture and design of IR-UWB networks are likely to differ significantly from narrow-band wireless networks. For the network to operate efficiently, it must be designed and implemented to take into account the features of IR-UWB and to take advantage of them. In this thesis, we focus on both the medium access control (MAC) layer and the physical layer. Our main objectives are to understand and determine (1) the architecture and design principles of IR-UWB networks, and (2) how to implement them in practical schemes. In the first part of this thesis, we explore the design space of IR-UWB networks and analyze the fundamental design choices. We show that interference from concurrent transmissions should not be prevented as in protocols that use mutual exclusion (for instance, IEEE 802.11). Instead, interference must be managed with rate adaptation, and an interference mitigation scheme should be used at the physical layer. Power control is useless. Based on these findings, we develop a practical PHY-aware MAC protocol that takes into account the specific nature of IR-UWB and that is able to adapt its rate to interference. We evaluate the performance obtained with this design: It clearly outperforms traditional designs that, instead, use mutual exclusion or power control. One crucial aspect of IR-UWB networks is packet detection and timing acquisition. In this context, a network design choice is whether to use a common or private acquisition preamble for timing acquisition. Therefore, we evaluate how this network design issue affects the network throughput. Our analysis shows that a private acquisition preamble yields a tremendous increase in throughput, compared with a common acquisition preamble. In addition, simulations on multi-hop topologies with TCP flows demonstrate that a network using private acquisition preambles has a stable throughput. On the contrary, using a common acquisition preamble exhibits an effect similar to exposed terminal issues in 802.11 networks: the throughput is severely degraded and flow starvation might occur. In the second part of this thesis, we are interested in IEEE 802.15.4a, a standard for low data-rate, low complexity networks that employs an IR-UWB physical layer. Due to its low complexity, energy detection is appealing for the implementation of practical receivers. But it is less robust to multi-user interference (MUI) than a coherent receiver. Hence, we evaluate the performance of an IEEE 802.15.4a physical layer with an energy detection receiver to find out whether a satisfactory performance is still obtained. Our results show that MUI severely degrades the performance in this case. The energy detection receiver significantly diminishes one of the most appealing benefits of UWB, specifically its robustness to MUI and thus the possibility of allowing for parallel transmissions. This performance analysis leads to the development of an IR-UWB receiver architecture, based on energy detection, that is robust to MUI and adapted to the peculiarities of IEEE 802.15.4a. This architecture greatly improves the performance and entails only a moderate increase in complexity. Finally, we present the architecture of an IR-UWB physical layer implementation in ns-2, a well-known network simulator. This architecture is generic and allows for the simulation of several multiple-access physical layers. In addition, it comprises a model of packet detection and timing acquisition. Network simulators also need to have efficient algorithms to accurately compute bit or packet error rates. Hence, we present a fast algorithm to compute the bit error rate of an IR-UWB physical layer in a network setting with MUI. It is based on a novel combination of large deviation theory and importance sampling.

EPFL2008

Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems

Zheng Dang, Pascal Fua, Yinlin Hu, Mathieu Salzmann, Fei Wang, Kwang Moo Yi

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector corresponding to the smallest, or zero, eigenvalue of a matrix representing a linear system. Incorporating this in deep learning frameworks would allow us to explicitly encode known notions of geometry, instead of having the network implicitly learn them from data. However, performing eigendecomposition within a network requires the ability to differentiate this operation. While theoretically doable, this introduces numerical instability in the optimization process in practice. In this paper, we introduce an eigendecomposition-free approach to training a deep network whose loss depends on the eigenvector corresponding to a zero eigenvalue of a matrix predicted by the network. We demonstrate that our approach is much more robust than explicit differentiation of the eigendecomposition using two general tasks, outlier rejection and denoising, with several practical examples including wide-baseline stereo, the perspective-n-point problem, and ellipse fitting. Empirically, our method has better convergence properties and yields state-of-the-art results.