57 research outputs found
Throughput-Delay Trade-off for Hierarchical Cooperation in Ad Hoc Wireless Networks
Hierarchical cooperation has recently been shown to achieve better throughput
scaling than classical multihop schemes under certain assumptions on the
channel model in static wireless networks. However, the end-to-end delay of
this scheme turns out to be significantly larger than those of multihop
schemes. A modification of the scheme is proposed here that achieves a
throughput-delay trade-off for T(n) between
and , where D(n) and T(n) are
respectively the average delay per bit and the aggregate throughput in a
network of n nodes. This trade-off complements the previous results of El Gamal
et al., which show that the throughput-delay trade-off for multihop schemes is
given by D(n)=T(n) where T(n) lies between and .
Meanwhile, the present paper considers the network multiple-access problem,
which may be of interest in its own right.Comment: 9 pages, 6 figures, to appear in IEEE Transactions on Information
Theory, submitted Dec 200
Wireless Network Simplification: the Gaussian N-Relay Diamond Network
We consider the Gaussian N-relay diamond network, where a source wants to
communicate to a destination node through a layer of N-relay nodes. We
investigate the following question: what fraction of the capacity can we
maintain by using only k out of the N available relays? We show that
independent of the channel configurations and the operating SNR, we can always
find a subset of k relays which alone provide a rate (kC/(k+1))-G, where C is
the information theoretic cutset upper bound on the capacity of the whole
network and G is a constant that depends only on N and k (logarithmic in N and
linear in k). In particular, for k = 1, this means that half of the capacity of
any N-relay diamond network can be approximately achieved by routing
information over a single relay. We also show that this fraction is tight:
there are configurations of the N-relay diamond network where every subset of k
relays alone can at most provide approximately a fraction k/(k+1) of the total
capacity. These high-capacity k-relay subnetworks can be also discovered
efficiently. We propose an algorithm that computes a constant gap approximation
to the capacity of the Gaussian N-relay diamond network in O(N log N) running
time and discovers a high-capacity k-relay subnetwork in O(kN) running time.
This result also provides a new approximation to the capacity of the Gaussian
N-relay diamond network which is hybrid in nature: it has both multiplicative
and additive gaps. In the intermediate SNR regime, this hybrid approximation is
tighter than existing purely additive or purely multiplicative approximations
to the capacity of this network.Comment: Submitted to Transactions on Information Theory in October 2012. The
new version includes discussions on the algorithmic complexity of discovering
a high-capacity subnetwork and on the performance of amplify-and-forwar
Feedback through Overhearing
In this paper we examine the value of feedback that comes from overhearing,
without dedicated feedback resources. We focus on a simple model for this
purpose: a deterministic two-hop interference channel, where feedback comes
from overhearing the forward-links. A new aspect brought by this setup is the
dual-role of the relay signal. While the relay signal needs to convey the
source message to its corresponding destination, it can also provide a feedback
signal which can potentially increase the capacity of the first hop. We derive
inner and outer bounds on the sum capacity which match for a large range of the
parameter values. Our results identify the parameter ranges where overhearing
can provide non-negative capacity gain and can even achieve the performance
with dedicated-feedback resources. The results also provide insights into which
transmissions are most useful to overhear
Can Feedback Increase the Capacity of the Energy Harvesting Channel?
We investigate if feedback can increase the capacity of an energy harvesting
communication channel where a transmitter powered by an exogenous energy
arrival process and equipped with a finite battery communicates to a receiver
over a memoryless channel. For a simple special case where the energy arrival
process is deterministic and the channel is a BEC, we explicitly compute the
feed-forward and feedback capacities and show that feedback can strictly
increase the capacity of this channel. Building on this example, we also show
that feedback can increase the capacity when the energy arrivals are i.i.d.
known noncausally at the transmitter and the receiver
Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks
n source and destination pairs randomly located in an area want to
communicate with each other. Signals transmitted from one user to another at
distance r apart are subject to a power loss of r^{-alpha}, as well as a random
phase. We identify the scaling laws of the information theoretic capacity of
the network. In the case of dense networks, where the area is fixed and the
density of nodes increasing, we show that the total capacity of the network
scales linearly with n. This improves on the best known achievability result of
n^{2/3} of Aeron and Saligrama, 2006. In the case of extended networks, where
the density of nodes is fixed and the area increasing linearly with n, we show
that this capacity scales as n^{2-alpha/2} for 2<alpha<3 and sqrt{n} for
alpha>3. The best known earlier result (Xie and Kumar 2006) identified the
scaling law for alpha > 4. Thus, much better scaling than multihop can be
achieved in dense networks, as well as in extended networks with low
attenuation. The performance gain is achieved by intelligent node cooperation
and distributed MIMO communication. The key ingredient is a hierarchical and
digital architecture for nodal exchange of information for realizing the
cooperation.Comment: 56 pages, 16 figures, submitted to IEEE Transactions on Information
Theor
Linear Capacity Scaling in Wireless Networks: Beyond Physical Limits?
We investigate the role of cooperation in wireless networks subject to a
spatial degrees of freedom limitation. To address the worst case scenario, we
consider a free-space line-of-sight type environment with no scattering and no
fading. We identify three qualitatively different operating regimes that are
determined by how the area of the network A, normalized with respect to the
wavelength lambda, compares to the number of users n. In networks with
sqrt{A}/lambda < sqrt{n}, the limitation in spatial degrees of freedom does not
allow to achieve a capacity scaling better than sqrt{n} and this performance
can be readily achieved by multi-hopping. This result has been recently shown
by Franceschetti et al. However, for networks with sqrt{A}/lambda > sqrt{n},
the number of available degrees of freedom is min(n, sqrt{A}/lambda), larger
that what can be achieved by multi-hopping. We show that the optimal capacity
scaling in this regime is achieved by hierarchical cooperation. In particular,
in networks with sqrt{A}/lambda> n, hierarchical cooperation can achieve linear
scaling.Comment: 10 pages, 5 figures, in Proc. of IEEE Information Theory and
Applications Workshop, Feb. 201
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