71,074 research outputs found
On Capacity and Optimal Scheduling for the Half-Duplex Multiple-Relay Channel
We study the half-duplex multiple-relay channel (HD-MRC) where every node can
either transmit or listen but cannot do both at the same time. We obtain a
capacity upper bound based on a max-flow min-cut argument and achievable
transmission rates based on the decode-forward (DF) coding strategy, for both
the discrete memoryless HD-MRC and the phase-fading HD-MRC. We discover that
both the upper bound and the achievable rates are functions of the
transmit/listen state (a description of which nodes transmit and which
receive). More precisely, they are functions of the time fraction of the
different states, which we term a schedule. We formulate the optimal scheduling
problem to find an optimal schedule that maximizes the DF rate. The optimal
scheduling problem turns out to be a maximin optimization, for which we propose
an algorithmic solution. We demonstrate our approach on a four-node
multiple-relay channel, obtaining closed-form solutions in certain scenarios.
Furthermore, we show that for the received signal-to-noise ratio degraded
phase-fading HD-MRC, the optimal scheduling problem can be simplified to a max
optimization.Comment: Author's final version (to appear in IEEE Transactions on Information
Theory
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
Unbiased sampling of network ensembles
Sampling random graphs with given properties is a key step in the analysis of
networks, as random ensembles represent basic null models required to identify
patterns such as communities and motifs. An important requirement is that the
sampling process is unbiased and efficient. The main approaches are
microcanonical, i.e. they sample graphs that match the enforced constraints
exactly. Unfortunately, when applied to strongly heterogeneous networks (like
most real-world examples), the majority of these approaches become biased
and/or time-consuming. Moreover, the algorithms defined in the simplest cases,
such as binary graphs with given degrees, are not easily generalizable to more
complicated ensembles. Here we propose a solution to the problem via the
introduction of a "Maximize and Sample" ("Max & Sam" for short) method to
correctly sample ensembles of networks where the constraints are `soft', i.e.
realized as ensemble averages. Our method is based on exact maximum-entropy
distributions and is therefore unbiased by construction, even for strongly
heterogeneous networks. It is also more computationally efficient than most
microcanonical alternatives. Finally, it works for both binary and weighted
networks with a variety of constraints, including combined degree-strength
sequences and full reciprocity structure, for which no alternative method
exists. Our canonical approach can in principle be turned into an unbiased
microcanonical one, via a restriction to the relevant subset. Importantly, the
analysis of the fluctuations of the constraints suggests that the
microcanonical and canonical versions of all the ensembles considered here are
not equivalent. We show various real-world applications and provide a code
implementing all our algorithms.Comment: MatLab code available at
http://www.mathworks.it/matlabcentral/fileexchange/46912-max-sam-package-zi
Universal and Robust Distributed Network Codes
Random linear network codes can be designed and implemented in a distributed
manner, with low computational complexity. However, these codes are classically
implemented over finite fields whose size depends on some global network
parameters (size of the network, the number of sinks) that may not be known
prior to code design. Also, if new nodes join the entire network code may have
to be redesigned.
In this work, we present the first universal and robust distributed linear
network coding schemes. Our schemes are universal since they are independent of
all network parameters. They are robust since if nodes join or leave, the
remaining nodes do not need to change their coding operations and the receivers
can still decode. They are distributed since nodes need only have topological
information about the part of the network upstream of them, which can be
naturally streamed as part of the communication protocol.
We present both probabilistic and deterministic schemes that are all
asymptotically rate-optimal in the coding block-length, and have guarantees of
correctness. Our probabilistic designs are computationally efficient, with
order-optimal complexity. Our deterministic designs guarantee zero error
decoding, albeit via codes with high computational complexity in general. Our
coding schemes are based on network codes over ``scalable fields". Instead of
choosing coding coefficients from one field at every node, each node uses
linear coding operations over an ``effective field-size" that depends on the
node's distance from the source node. The analysis of our schemes requires
technical tools that may be of independent interest. In particular, we
generalize the Schwartz-Zippel lemma by proving a non-uniform version, wherein
variables are chosen from sets of possibly different sizes. We also provide a
novel robust distributed algorithm to assign unique IDs to network nodes.Comment: 12 pages, 7 figures, 1 table, under submission to INFOCOM 201
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
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