3,588 research outputs found
The Sensing Capacity of Sensor Networks
This paper demonstrates fundamental limits of sensor networks for detection
problems where the number of hypotheses is exponentially large. Such problems
characterize many important applications including detection and classification
of targets in a geographical area using a network of sensors, and detecting
complex substances with a chemical sensor array. We refer to such applications
as largescale detection problems. Using the insight that these problems share
fundamental similarities with the problem of communicating over a noisy
channel, we define a quantity called the sensing capacity and lower bound it
for a number of sensor network models. The sensing capacity expression differs
significantly from the channel capacity due to the fact that a fixed sensor
configuration encodes all states of the environment. As a result, codewords are
dependent and non-identically distributed. The sensing capacity provides a
bound on the minimal number of sensors required to detect the state of an
environment to within a desired accuracy. The results differ significantly from
classical detection theory, and provide an ntriguing connection between sensor
networks and communications. In addition, we discuss the insight that sensing
capacity provides for the problem of sensor selection.Comment: Submitted to IEEE Transactions on Information Theory, November 200
Gossip Algorithms for Distributed Signal Processing
Gossip algorithms are attractive for in-network processing in sensor networks
because they do not require any specialized routing, there is no bottleneck or
single point of failure, and they are robust to unreliable wireless network
conditions. Recently, there has been a surge of activity in the computer
science, control, signal processing, and information theory communities,
developing faster and more robust gossip algorithms and deriving theoretical
performance guarantees. This article presents an overview of recent work in the
area. We describe convergence rate results, which are related to the number of
transmitted messages and thus the amount of energy consumed in the network for
gossiping. We discuss issues related to gossiping over wireless links,
including the effects of quantization and noise, and we illustrate the use of
gossip algorithms for canonical signal processing tasks including distributed
estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation
Sensor networks potentially feature large numbers of nodes that can sense
their environment over time, communicate with each other over a wireless
network, and process information. They differ from data networks in that the
network as a whole may be designed for a specific application. We study the
theoretical foundations of such large scale sensor networks, addressing four
fundamental issues- connectivity, capacity, clocks and function computation.
To begin with, a sensor network must be connected so that information can
indeed be exchanged between nodes. The connectivity graph of an ad-hoc network
is modeled as a random graph and the critical range for asymptotic connectivity
is determined, as well as the critical number of neighbors that a node needs to
connect to. Next, given connectivity, we address the issue of how much data can
be transported over the sensor network. We present fundamental bounds on
capacity under several models, as well as architectural implications for how
wireless communication should be organized.
Temporal information is important both for the applications of sensor
networks as well as their operation.We present fundamental bounds on the
synchronizability of clocks in networks, and also present and analyze
algorithms for clock synchronization. Finally we turn to the issue of gathering
relevant information, that sensor networks are designed to do. One needs to
study optimal strategies for in-network aggregation of data, in order to
reliably compute a composite function of sensor measurements, as well as the
complexity of doing so. We address the issue of how such computation can be
performed efficiently in a sensor network and the algorithms for doing so, for
some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE
Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach
This paper addresses network code design for robust transmission of sources
over an orthogonal two-hop wireless network with a broadcasting relay. The
network consists of multiple sources and destinations in which each
destination, benefiting the relay signal, intends to decode a subset of the
sources. Two special instances of this network are orthogonal broadcast relay
channel and the orthogonal multiple access relay channel. The focus is on
complexity constrained scenarios, e.g., for wireless sensor networks, where
channel coding is practically imperfect. Taking a source-channel and network
coding approach, we design the network code (mapping) at the relay such that
the average reconstruction distortion at the destinations is minimized. To this
end, by decomposing the distortion into its components, an efficient design
algorithm is proposed. The resulting network code is nonlinear and
substantially outperforms the best performing linear network code. A motivating
formulation of a family of structured nonlinear network codes is also
presented. Numerical results and comparison with linear network coding at the
relay and the corresponding distortion-power bound demonstrate the
effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio
Distributed Remote Vector Gaussian Source Coding with Covariance Distortion Constraints
In this paper, we consider a distributed remote source coding problem, where
a sequence of observations of source vectors is available at the encoder. The
problem is to specify the optimal rate for encoding the observations subject to
a covariance matrix distortion constraint and in the presence of side
information at the decoder. For this problem, we derive lower and upper bounds
on the rate-distortion function (RDF) for the Gaussian case, which in general
do not coincide. We then provide some cases, where the RDF can be derived
exactly. We also show that previous results on specific instances of this
problem can be generalized using our results. We finally show that if the
distortion measure is the mean squared error, or if it is replaced by a certain
mutual information constraint, the optimal rate can be derived from our main
result.Comment: This is the final version accepted at ISIT'1
Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks
A model, called the linear transform network (LTN), is proposed to analyze
the compression and estimation of correlated signals transmitted over directed
acyclic graphs (DAGs). An LTN is a DAG network with multiple source and
receiver nodes. Source nodes transmit subspace projections of random correlated
signals by applying reduced-dimension linear transforms. The subspace
projections are linearly processed by multiple relays and routed to intended
receivers. Each receiver applies a linear estimator to approximate a subset of
the sources with minimum mean squared error (MSE) distortion. The model is
extended to include noisy networks with power constraints on transmitters. A
key task is to compute all local compression matrices and linear estimators in
the network to minimize end-to-end distortion. The non-convex problem is solved
iteratively within an optimization framework using constrained quadratic
programs (QPs). The proposed algorithm recovers as special cases the regular
and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the
distortion region of multi-source, multi-receiver networks are given for linear
coding based on convex relaxations. Cut-set lower bounds are also given for any
coding strategy based on information theory. The distortion region and
compression-estimation tradeoffs are illustrated for different communication
demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal
Processin
- …