95,065 research outputs found
Network Information Flow in Small World Networks
Recent results from statistical physics show that large classes of complex
networks, both man-made and of natural origin, are characterized by high
clustering properties yet strikingly short path lengths between pairs of nodes.
This class of networks are said to have a small-world topology. In the context
of communication networks, navigable small-world topologies, i.e. those which
admit efficient distributed routing algorithms, are deemed particularly
effective, for example in resource discovery tasks and peer-to-peer
applications. Breaking with the traditional approach to small-world topologies
that privileges graph parameters pertaining to connectivity, and intrigued by
the fundamental limits of communication in networks that exploit this type of
topology, we investigate the capacity of these networks from the perspective of
network information flow. Our contribution includes upper and lower bounds for
the capacity of standard and navigable small-world models, and the somewhat
surprising result that, with high probability, random rewiring does not alter
the capacity of a small-world network.Comment: 23 pages, 8 fitures, submitted to the IEEE Transactions on
Information Theory, November 200
Product Multicommodity Flow in Wireless Networks
We provide a tight approximate characterization of the -dimensional
product multicommodity flow (PMF) region for a wireless network of nodes.
Separate characterizations in terms of the spectral properties of appropriate
network graphs are obtained in both an information theoretic sense and for a
combinatorial interference model (e.g., Protocol model). These provide an inner
approximation to the dimensional capacity region. These results answer
the following questions which arise naturally from previous work: (a) What is
the significance of in the scaling laws for the Protocol
interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a
tight approximation to the "maximum supportable flow" for node distributions
more general than the geometric random distribution, traffic models other than
randomly chosen source-destination pairs, and under very general assumptions on
the channel fading model?
We first establish that the random source-destination model is essentially a
one-dimensional approximation to the capacity region, and a special case of
product multi-commodity flow. Building on previous results, for a combinatorial
interference model given by a network and a conflict graph, we relate the
product multicommodity flow to the spectral properties of the underlying graphs
resulting in computational upper and lower bounds. For the more interesting
random fading model with additive white Gaussian noise (AWGN), we show that the
scaling laws for PMF can again be tightly characterized by the spectral
properties of appropriately defined graphs. As an implication, we obtain
computationally efficient upper and lower bounds on the PMF for any wireless
network with a guaranteed approximation factor.Comment: Revised version of "Capacity-Delay Scaling in Arbitrary Wireless
Networks" submitted to the IEEE Transactions on Information Theory. Part of
this work appeared in the Allerton Conference on Communication, Control, and
Computing, Monticello, IL, 2005, and the Internation Symposium on Information
Theory (ISIT), 200
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
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