Function Computation over Networks

This thesis looks at efficient information processing for two network applications: content delivery with caching and collecting summary statistics in wireless sensor networks. Both applications are studied under the same paradigm: function computation over networks, where distributed source nodes cooperatively communicate some functions of individual observations to one or multiple destinations. One approach that always works is to convey all observations and then let the destinations compute the desired functions by themselves. However, if the available communication resources are limited, then revealing less unwanted information becomes critical. Centered on this goal, this thesis develops new coding schemes using information-theoretic tools.

The first part of this thesis focuses on content delivery with caching. Caching is a technique that facilitates reallocation of communication resources in order to avoid network congestion during peak-traffic times. An information-theoretic model, termed sequential coding for computing, is proposed to analyze the potential gains offered by the caching technique. For the single-user case, the proposed framework succeeds in verifying the optimality of some simple caching strategies and in providing guidance towards optimal caching strategies. For the two-user case, five representative subproblems are considered, which draw connections with classic source coding problems including the Gray-Wyner system, successive refinement, and the Kaspi/Heegard-Berger problem. Afterwards, the problem of distributed computing with successive refinement is considered. It is shown that if full data recovery is required in the second stage of successive refinement, then any information acquired in the first stage will be useful later in the second stage.

The second part of this thesis looks at the collection of summary statistics in wireless sensor networks. Summary statistics include arithmetic mean, median, standard deviation, etc, and they belong to the class of symmetric functions. This thesis develops arithmetic computation coding in order to efficiently perform in-network computation for weighted arithmetic sums and symmetric functions. The developed arithmetic computation coding increases the achievable computation rate from $\Theta((\log L)/L)$ to $\Theta(1/\log L)$ , where $L$ is the number of sensors. Finally, this thesis demonstrates that interaction among sensors is beneficial for computation of type-threshold functions, e.g., the maximum and the indicator function, and that a non-vanishing computation rate is achievable.

Efficient decentralized communications in sensor networks

Razvan Cristescu

This thesis is concerned with problems in decentralized communication in large networks. Namely, we address the problems of joint rate allocation and transmission of data sources measured at nodes, and of controlling the multiple access of sources to a shared medium. In our study, we consider in particular the important case of a sensor network measuring correlated data. In the first part of this thesis, we consider the problem of correlated data gathering by a network with a sink node and a tree communication structure, where the goal is to minimize the total transmission cost of transporting the information collected by the nodes, to the sink node. Two coding strategies are analyzed: a Slepian-Wolf model where optimal coding is complex and transmission optimization is simple, and a joint entropy coding model with explicit communication where coding is simple and transmission optimization is difficult. This problem requires a joint optimization of the rate allocation at the nodes and of the transmission structure. For the Slepian-Wolf setting, we derive a closed form solution and an efficient distributed approximation algorithm with a good performance. We generalize our results to the case of multiple sinks. For the explicit communication case, we prove that building an optimal data gathering tree is NP-complete and we propose various distributed approximation algorithms. We compare asymptotically, for dense networks, the total costs associated with Slepian-Wolf coding and explicit communication, by finding their corresponding scaling laws and analyzing the ratio of their respective costs. We argue that, for large networks and under certain conditions on the correlation structure, "intelligent", but more complex Slepian-Wolf coding provides unbounded gains over the widely used straightforward approach of opportunistic aggregation and compression by explicit communication. In the second part of this thesis, we consider a queuing problem in which the service rate of a queue is a function of a partially observed Markov chain, and in which the arrivals are controlled based on those partial observations so as to keep the system in a desirable mildly unstable regime. The optimal controller for this problem satisfies a separation property: we first compute a probability measure on the state space of the chain, namely the information state, then use this measure as the new state based on which to make control decisions. We give a formal description of the system considered and of its dynamics, we formalize and solve an optimal control problem, and we show numerical simulations to illustrate with concrete examples properties of the optimal control law. We show how the ergodic behavior of our queuing model is characterized by an invariant measure over all possible information states, and we construct that measure. Our results may be applied for designing efficient and stable algorithms for medium access control in multiple accessed systems, in particular for sensor networks.

EPFL2004

Fundamental limits and optimal operation in large wireless networks

Ayfer Özgür Aydin

Wireless adhoc networks consist of users that want to communicate with each other over a shared wireless medium. The users have transmitting and receiving capabilities but there is no additional infrastructure for assisting communication. This is in contrast to existing wireless systems, cellular networks for example, where communication between wireless users heavily relies on an additional infrastructure of base stations connected with a high-capacity wired backbone. The fact that they are infrastructureless makes wireless adhoc networks inexpensive, easy to build and robust but at the same time technically more challenging. The fundamental challenge is how to deal with interference: many simultaneous transmissions have to be accommodated on the same wireless channel when each of these transmissions constitutes interference for the others, degrading the quality of the communication. The traditional approach to wireless adhoc networks is to organize users so that they relay information for each other in a multi-hop fashion. Such multi-hopping strategies face scalability problems at large system size. As shown by Gupta and Kumar in their seminal work in 2000, the maximal communication rate per user under such strategies scales inversely proportional to the square root of the number of users in the network, hence decreases to zero with increasing system size. This limitation is due to interference that precludes having many simultaneous point-to-point transmissions inside the network. In this thesis, we propose a multiscale hierarchical cooperation architecture for distributed MIMO communication in wireless adhoc networks. This novel architecture removes the interference limitation at least as far as scaling is concerned: we show that the per-user communication rate under this strategy does not degrade significantly even if there are more and more users entering into the network. This is in sharp contrast to the performance achieved by the classical multi-hopping schemes. However, the overall picture is much richer than what can be depicted by a single scheme or a single scaling law formula. Nowadays, wireless adhoc networks are considered for a wide range of practical applications and this translates to having a number of system parameters (e.g., area, power, bandwidth) with large operational range. Different applications lie in different parameter ranges and can therefore exhibit different characteristics. A thorough understanding of wireless adhoc networks can only be obtained by exploring the whole parameter space. Existing scaling law formulations are insufficient for this purpose as they concentrate on very small subsets of the system parameters. We propose a new scaling law formulation for wireless adhoc networks that serves as a mathematical tool to characterize their fundamental operating regimes. For the standard wireless channel model where signals are subject to power path-loss attenuation and random phase changes, we identify four qualitatively different operating regimes in wireless adhoc networks with large number of users. In each of these regimes, we characterize the dependence of the capacity on major system parameters. In particular, we clarify the impact of the power and bandwidth limitations on performance. This is done by deriving upper bounds on the information theoretic capacity of wireless adhoc networks in Chapter 3, and constructing communication schemes that achieve these upper bounds in Chapter 4. Our analysis identifies three engineering quantities that together determine the operating regime of a given wireless network: the short-distance signal-to-noise power ratio (SNRs), the long-distance signal-to-noise power ratio (SNRl) and the power path-loss exponent of the environment. The right communication strategy for a given application is dictated by its operating regime. We show that conventional multi-hopping schemes are optimal when the power path-loss exponent of the environment is larger than 3 and SNRs ≪ 0 dB. Such networks are extremely power-limited. On the other hand, the novel architecture proposed in this thesis, based on hierarchical cooperation and distributed MIMO, is the fundamentally right strategy for wireless networks with SNRl ≫ 0 dB. Such networks experience no power limitation. In the intermediate cases, captured by the remaining two operating regimes, neither multi-hopping nor hierarchical-MIMO achieves optimal performance. We construct new schemes for these regimes that achieve capacity. The proposed characterization of wireless adhoc networks in terms of their fundamental operating regimes, is analogous to the familiar understanding of the two operating regimes of the point-to-point additive white Gaussian noise (AWGN) channel. From an engineering point of view, one of the most important contributions of Shannon's celebrated capacity formula is to identify two qualitatively different operating regimes on this channel. Determined by its signal-to-noise power ratio (SNR), an AWGN channel can be either in a bandwidth-limited (SNR ≫ 0 dB) or a power-limited (SNR ≪ 0 dB) regime. Communication system design for this channel has been primarily driven by the operating regime one is in.

EPFL2009

Signaling and Reciprocity

Wojciech Galuba

Complex networks exist for a number of purposes. The neural, metabolic and food networks ensure our survival, while the social, economic, transportation and communication networks allow us to prosper. Independently of the purposes and particularities of the physical embodiment of the networks, one of their fundamental functions is the delivery of information from one part of the network to another. Gossip and diseases diffuse in the social networks, electrochemical signals propagate in the neural networks and data packets travel in the Internet. Engineering networks for robust information flows is a challenging task. First, the mechanism through which the network forms and changes its topology needs to be defined. Second, within a given topology, the information must be routed to the appropriate recipients. Third, both the network formation and the routing mechanisms need to be robust against a wide spectrum of failures and adversaries. Fourth, the network formation, routing and failure recovery must operate under the resource constraints, either intrinsic or extrinsic to the network. Finally, the autonomously operating parts of the network must be incentivized to contribute their resources to facilitate the information flows. This thesis tackles the above challenges within the context of several types of networks: 1) peer-to-peer overlays – computers interconnected over the Internet to form an overlay in which participants provide various services to one another, 2) mobile ad-hoc networks – mobile nodes distributed in physical space communicating wirelessly with the goal of delivering data from one part of the network to another, 3) file-sharing networks – networks whose participants interconnect over the Internet to exchange files, 4) social networks – humans disseminating and consuming information through the network of social relationships. The thesis makes several contributions. Firstly, we propose a general algorithm, which given a set of nodes embedded in an arbitrary metric space, interconnects them into a network that efficiently routes information. We apply the algorithm to the peer-to-peer overlays and experimentally demonstrate its high performance, scalability as well as resilience to continuous peer arrivals and departures. We then shift our focus to the problem of the reliability of routing in the peer-to-peer overlays. Each overlay peer has limited resources and when they are exhausted this ultimately leads to delayed or lost overlay messages. All the solutions addressing this problem rely on message redundancy, which significantly increases the resource costs of fault-tolerance. We propose a bandwidth-efficient single-path Forward Feedback Protocol (FFP) for overlay message routing in which successfully delivered messages are followed by a feedback signal to reinforce the routing paths. Internet testbed evaluation shows that FFP uses 2-5 times less network bandwidth than the existing protocols relying on message redundancy, while achieving comparable fault-tolerance levels under a variety of failure scenarios. While the Forward Feedback Protocol is robust to message loss and delays, it is vulnerable to malicious message injection. We address this and other security problems by proposing Castor, a variant of FFP for mobile ad-hoc networks (MANETs). In Castor, we use the same general mechanism as in FFP; each time a message is routed, the routing path is either enforced or weakened by the feedback signal depending on whether the routing succeeded or not. However, unlike FFP, Castor employs cryptographic mechanisms for ensuring the integrity and authenticity of the messages. We compare Castor to four other MANET routing protocols. Despite Castor's simplicity, it achieves up to 40% higher packet delivery rates than the other protocols and recovers at least twice as fast as the other protocols in a wide range of attacks and failure scenarios. Both of our protocols, FFP and Castor, rely on simple signaling to improve the routing robustness in peer-to-peer and mobile ad-hoc networks. Given the success of the signaling mechanism in shaping the information flows in these two types of networks, we examine if signaling plays a similar crucial role in the on-line social networks. We characterize the propagation of URLs in the social network of Twitter. The data analysis uncovers several statistical regularities in the user activity, the social graph, the structure of the URL cascades as well as the communication and signaling dynamics. Based on these results, we propose a propagation model that accurately predicts which users are likely to mention which URLs. We outline a number of applications where the social network information flow modelling would be crucial: content ranking and filtering, viral marketing and spam detection. Finally, we consider the problem of freeriding in peer-to-peer file-sharing applications, when users can download data from others, but never reciprocate by uploading. To address the problem, we propose a variant of the BitTorrent system in which two peers are only allowed to connect if their owners know one another in the real world. When the users know which other users their BitTorrent client connects to, they are more likely to cooperate. The social network becomes the content distribution network and the freeriding problem is solved by leveraging the social norms and reciprocity to stabilize cooperation rather than relying on technological means. Our extensive simulation shows that the social network topology is an efficient and scalable content distribution medium, while at the same time provides robustness to freeriding.

EPFL2011