124 research outputs found
A Geometric Framework for Investigating the Multiple Unicast Network Coding Conjecture
The multiple unicast network coding conjecture states that for multiple unicast sessions in an undirected network, network coding is equivalent to routing. Simple and intuitive as it appears, the conjecture has remained open since its proposal in 2004 [1], [2], and is now a well-known unsolved problem in the field of network coding. Based on a recently proposed tool of space information flow [3]-[5], we present a geometric framework for analyzing the multiple unicast conjecture. The framework consists of four major steps, in which the conjecture is transformed from its throughput version to cost version, from the graph domain to the space domain, and then from high dimension to 1-D, where it is to be eventually proved. We apply the geometric framework to derive unified proofs to known results of the conjecture, as well as new results previously unknown. A possible proof to the conjecture based on this framework is outlined.published_or_final_versio
An asymptotically optimal push-pull method for multicasting over a random network
We consider allcast and multicast flow problems where either all of the nodes
or only a subset of the nodes may be in session. Traffic from each node in the
session has to be sent to every other node in the session. If the session does
not consist of all the nodes, the remaining nodes act as relays. The nodes are
connected by undirected links whose capacities are independent and identically
distributed random variables. We study the asymptotics of the capacity region
(with network coding) in the limit of a large number of nodes, and show that
the normalized sum rate converges to a constant almost surely. We then provide
a decentralized push-pull algorithm that asymptotically achieves this
normalized sum rate without network coding.Comment: 13 pages, extended version of paper presented at the IEEE
International Symposium on Information Theory (ISIT) 2012, minor revision to
text to address review comments, to appear in IEEE Transactions in
information theor
On the multiple unicast capacity of 3-source, 3-terminal directed acyclic networks
We consider the multiple unicast problem with three source-terminal pairs
over directed acyclic networks with unit-capacity edges. The three
pairs wish to communicate at unit-rate via network coding. The connectivity
between the pairs is quantified by means of a connectivity level
vector, such that there exist edge-disjoint paths between
and . In this work we attempt to classify networks based on the
connectivity level. It can be observed that unit-rate transmission can be
supported by routing if , for all . In this work,
we consider, connectivity level vectors such that . We present either a constructive linear network coding scheme or an
instance of a network that cannot support the desired unit-rate requirement,
for all such connectivity level vectors except the vector (and its
permutations). The benefits of our schemes extend to networks with higher and
potentially different edge capacities. Specifically, our experimental results
indicate that for networks where the different source-terminal paths have a
significant overlap, our constructive unit-rate schemes can be packed along
with routing to provide higher throughput as compared to a pure routing
approach.Comment: To appear in the IEEE/ACM Transactions on Networkin
Network Coding: Exploiting Broadcast and Superposition in Wireless Networks
In this thesis we investigate improvements in efficiency of wireless communication networks, based on methods that are fundamentally different from the principles that form the basis of state-of-the-art technology. The first difference is that broadcast and superposition are exploited instead of reducing the wireless medium to a network of point-to-point links. The second difference is that the problem of transporting information through the network is not treated as a flow problem. Instead we allow for network coding to be used.\ud
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First, we consider multicast network coding in settings where the multicast configuration changes over time. We show that for certain problem classes a universal network code can be constructed. One application is to efficiently tradeoff throughput against cost.\ud
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Next, we deal with increasing energy efficiency by means of network coding in the presence of broadcast. It is demonstrated that for multiple unicast traffic in networks with nodes arranged on two and three dimensional rectangular lattices, network coding can reduce energy consumption by factors of four and six, respectively, compared to routing.\ud
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Finally, we consider the use of superposition by allowing nodes to decode sums of messages. We introduce different deterministic models of wireless networks, representing various ways of handling broadcast and superposition. We provide lower and upper bounds on the transport capacity under these models. For networks with nodes arranged on a hexagonal lattice it is found that the capacity under a model exploiting both broadcast and superposition is at least 2.5 times, and no more than six times, the transport capacity under a model of point-to-point links
Classifying Networks For Network Coding
Network coding is a relatively recent development in the realm of maximizing information
transfer in communications and computer networks. Traditional networks operate by simply
storing and forwarding data along. Network coding, however, allows intermediate network
nodes to combine data using arithmetic operations. In many instances, this can lead
to more efficient use of network resources. Since there is a significant throughput input in
some networks, some studies have been done on what kinds of networks will benefit from
coding. A coding advantage is defined as a situation where a network coded graph has a
lower cost to send given information per unit time session than the same un-coded graph. It
has been proven that for two simple single-sender-single-receiver communication sessions
that a graph must have one of two special graph-theoretic structures called the butterfly and
grail in order to yield a coding advantage. We decided to focus our efforts on a different
traffic scenario: a multicast session with a single sender and multiple receivers. Through
our research we proved that a multicast-version of the butterfly network structure is needed
within a single session multicast with two sinks and one source in order to gain a coding
advantage. We also performed a simulation-based study in order to study the structures of
multicast sessions with a larger number of receivers. The study involved the random generation
of networks using several graph generation techniques. We also considered a variety
of different edge-weighting constraints. Given a particular graph with set edge weights, the
coding advantage problem was modeled as a linear program and run through the simulator
to determine if a coding advantage was gained. Based on visual inspection of these results,
it appears that variations of the multicast butterfly are ultimately the dominant structure
allowing for a coding advantage. We also found that many types of random networks only
very rarely resulted in a coding advantage. Only the graphs generated using the rectangular
grid method showed a coding advantage, with a coding advantage percentage of 0.005%
for 4 sinks in a 30 node network, with the coding advantage percentage going up as the
number of sinks within the network increased
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