11,470 research outputs found
Formal analysis techniques for gossiping protocols
We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them
The age of information in gossip networks
We introduce models of gossip based communication networks in which each node
is simultaneously a sensor, a relay and a user of information. We model the
status of ages of information between nodes as a discrete time Markov chain. In
this setting a gossip transmission policy is a decision made at each node
regarding what type of information to relay at any given time (if any). When
transmission policies are based on random decisions, we are able to analyze the
age of information in certain illustrative structured examples either by means
of an explicit analysis, an algorithm or asymptotic approximations. Our key
contribution is presenting this class of models.Comment: 15 pages, 8 figure
Distributed Detection and Estimation in Wireless Sensor Networks
In this article we consider the problems of distributed detection and
estimation in wireless sensor networks. In the first part, we provide a general
framework aimed to show how an efficient design of a sensor network requires a
joint organization of in-network processing and communication. Then, we recall
the basic features of consensus algorithm, which is a basic tool to reach
globally optimal decisions through a distributed approach. The main part of the
paper starts addressing the distributed estimation problem. We show first an
entirely decentralized approach, where observations and estimations are
performed without the intervention of a fusion center. Then, we consider the
case where the estimation is performed at a fusion center, showing how to
allocate quantization bits and transmit powers in the links between the nodes
and the fusion center, in order to accommodate the requirement on the maximum
estimation variance, under a constraint on the global transmit power. We extend
the approach to the detection problem. Also in this case, we consider the
distributed approach, where every node can achieve a globally optimal decision,
and the case where the decision is taken at a central node. In the latter case,
we show how to allocate coding bits and transmit power in order to maximize the
detection probability, under constraints on the false alarm rate and the global
transmit power. Then, we generalize consensus algorithms illustrating a
distributed procedure that converges to the projection of the observation
vector onto a signal subspace. We then address the issue of energy consumption
in sensor networks, thus showing how to optimize the network topology in order
to minimize the energy necessary to achieve a global consensus. Finally, we
address the problem of matching the topology of the network to the graph
describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R.
Chellapa and S. Theodoridis, Eds., Elsevier, 201
Convergence Speed of the Consensus Algorithm with Interference and Sparse Long-Range Connectivity
We analyze the effect of interference on the convergence rate of average
consensus algorithms, which iteratively compute the measurement average by
message passing among nodes. It is usually assumed that these algorithms
converge faster with a greater exchange of information (i.e., by increased
network connectivity) in every iteration. However, when interference is taken
into account, it is no longer clear if the rate of convergence increases with
network connectivity. We study this problem for randomly-placed
consensus-seeking nodes connected through an interference-limited network. We
investigate the following questions: (a) How does the rate of convergence vary
with increasing communication range of each node? and (b) How does this result
change when each node is allowed to communicate with a few selected far-off
nodes? When nodes schedule their transmissions to avoid interference, we show
that the convergence speed scales with , where is the
communication range and is the number of dimensions. This scaling is the
result of two competing effects when increasing : Increased schedule length
for interference-free transmission vs. the speed gain due to improved
connectivity. Hence, although one-dimensional networks can converge faster from
a greater communication range despite increased interference, the two effects
exactly offset one another in two-dimensions. In higher dimensions, increasing
the communication range can actually degrade the rate of convergence. Our
results thus underline the importance of factoring in the effect of
interference in the design of distributed estimation algorithms.Comment: 27 pages, 4 figure
Consensus Propagation
We propose consensus propagation, an asynchronous distributed protocol for
averaging numbers across a network. We establish convergence, characterize the
convergence rate for regular graphs, and demonstrate that the protocol exhibits
better scaling properties than pairwise averaging, an alternative that has
received much recent attention. Consensus propagation can be viewed as a
special case of belief propagation, and our results contribute to the belief
propagation literature. In particular, beyond singly-connected graphs, there
are very few classes of relevant problems for which belief propagation is known
to converge.Comment: journal versio
Geographic Gossip: Efficient Averaging for Sensor Networks
Gossip algorithms for distributed computation are attractive due to their
simplicity, distributed nature, and robustness in noisy and uncertain
environments. However, using standard gossip algorithms can lead to a
significant waste in energy by repeatedly recirculating redundant information.
For realistic sensor network model topologies like grids and random geometric
graphs, the inefficiency of gossip schemes is related to the slow mixing times
of random walks on the communication graph. We propose and analyze an
alternative gossiping scheme that exploits geographic information. By utilizing
geographic routing combined with a simple resampling method, we demonstrate
substantial gains over previously proposed gossip protocols. For regular graphs
such as the ring or grid, our algorithm improves standard gossip by factors of
and respectively. For the more challenging case of random
geometric graphs, our algorithm computes the true average to accuracy
using radio
transmissions, which yields a factor improvement over
standard gossip algorithms. We illustrate these theoretical results with
experimental comparisons between our algorithm and standard methods as applied
to various classes of random fields.Comment: To appear, IEEE Transactions on Signal Processin
Network Information Flow with Correlated Sources
In this paper, we consider a network communications problem in which multiple
correlated sources must be delivered to a single data collector node, over a
network of noisy independent point-to-point channels. We prove that perfect
reconstruction of all the sources at the sink is possible if and only if, for
all partitions of the network nodes into two subsets S and S^c such that the
sink is always in S^c, we have that H(U_S|U_{S^c}) < \sum_{i\in S,j\in S^c}
C_{ij}. Our main finding is that in this setup a general source/channel
separation theorem holds, and that Shannon information behaves as a classical
network flow, identical in nature to the flow of water in pipes. At first
glance, it might seem surprising that separation holds in a fairly general
network situation like the one we study. A closer look, however, reveals that
the reason for this is that our model allows only for independent
point-to-point channels between pairs of nodes, and not multiple-access and/or
broadcast channels, for which separation is well known not to hold. This
``information as flow'' view provides an algorithmic interpretation for our
results, among which perhaps the most important one is the optimality of
implementing codes using a layered protocol stack.Comment: Final version, to appear in the IEEE Transactions on Information
Theory -- contains (very) minor changes based on the last round of review
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