15,383 research outputs found
Asymptotic Sum-Capacity of Random Gaussian Interference Networks Using Interference Alignment
We consider a dense n-user Gaussian interference network formed by paired
transmitters and receivers placed independently at random in Euclidean space.
Under natural conditions on the node position distributions and signal
attenuation, we prove convergence in probability of the average per-user
capacity C_Sigma/n to 1/2 E log(1 + 2SNR).
The achievability result follows directly from results based on an
interference alignment scheme presented in recent work of Nazer et al. Our main
contribution comes through the converse result, motivated by ideas of
`bottleneck links' developed in recent work of Jafar. An information theoretic
argument gives a capacity bound on such bottleneck links, and probabilistic
counting arguments show there are sufficiently many such links to tightly bound
the sum-capacity of the whole network.Comment: 5 pages; to appear at ISIT 201
Smooth Multirate Multicast Congestion Control
A significant impediment to deployment of multicast services is the daunting technical complexity of developing, testing and validating congestion control protocols ïŹt for wide-area deployment. Protocols such as pgmcc and TFMCC have recently made considerable progress on the single rate case, i.e. where one dynamic reception rate is maintained for all receivers in the session. However, these protocols have limited applicability, since scaling to session sizes beyond tens of participants necessitates the use of multiple rate protocols. Unfortunately, while existing multiple rate protocols exhibit better scalability, they are both less mature than single rate protocols and suffer from high complexity.
We propose a new approach to multiple rate congestion control that leverages proven single rate congestion control methods by orchestrating an ensemble of independently controlled single rate sessions. We describe SMCC, a new multiple rate equation-based congestion control algorithm for layered multicast sessions that employs TFMCC as the primary underlying control mechanism for each layer. SMCC combines the benefits of TFMCC (smooth rate control, equation-based TCP friendliness) with the scalability and flexibility of multiple rates to provide a sound multiple rate multicast congestion control policy.National Science Foundation (ANI-9986397, ANI-0092196
Absence of phase coexistence in disordered exclusion processes with bypassing
Adding quenched disorder to the one-dimensional asymmetric exclusion process
is known to always induce phase separation. To test the robustness of this
result, we introduce two modifications of the process that allow particles to
bypass defect sites. In the first case, particles are allowed to jump l sites
ahead with the probability p_l ~ l^-(1+sigma), where sigma>1. By using Monte
Carlo simulations and the mean-field approach, we show that phase coexistence
may be absent up to enormously large system sizes, e.g. lnL~50, but is present
in the thermodynamic limit, as in the short-range case. In the second case, we
consider the exclusion process on a quadratic lattice with symmetric and
totally asymmetric hopping perpendicular to and along the direction of driving,
respectively. We show that in an anisotropic limit of this model a regime may
be found where phase coexistence is absent.Comment: 18 pages, 10 figures, to appear in JSTA
Interference Mitigation in Large Random Wireless Networks
A central problem in the operation of large wireless networks is how to deal
with interference -- the unwanted signals being sent by transmitters that a
receiver is not interested in. This thesis looks at ways of combating such
interference.
In Chapters 1 and 2, we outline the necessary information and communication
theory background, including the concept of capacity. We also include an
overview of a new set of schemes for dealing with interference known as
interference alignment, paying special attention to a channel-state-based
strategy called ergodic interference alignment.
In Chapter 3, we consider the operation of large regular and random networks
by treating interference as background noise. We consider the local performance
of a single node, and the global performance of a very large network.
In Chapter 4, we use ergodic interference alignment to derive the asymptotic
sum-capacity of large random dense networks. These networks are derived from a
physical model of node placement where signal strength decays over the distance
between transmitters and receivers. (See also arXiv:1002.0235 and
arXiv:0907.5165.)
In Chapter 5, we look at methods of reducing the long time delays incurred by
ergodic interference alignment. We analyse the tradeoff between reducing delay
and lowering the communication rate. (See also arXiv:1004.0208.)
In Chapter 6, we outline a problem that is equivalent to the problem of
pooled group testing for defective items. We then present some new work that
uses information theoretic techniques to attack group testing. We introduce for
the first time the concept of the group testing channel, which allows for
modelling of a wide range of statistical error models for testing. We derive
new results on the number of tests required to accurately detect defective
items, including when using sequential `adaptive' tests.Comment: PhD thesis, University of Bristol, 201
An asymptotic existence result on compressed sensing matrices
For any rational number and all sufficiently large we give a
deterministic construction for an compressed
sensing matrix with -recoverability where . Our
method uses pairwise balanced designs and complex Hadamard matrices in the
construction of -equiangular frames, which we introduce as a
generalisation of equiangular tight frames. The method is general and produces
good compressed sensing matrices from any appropriately chosen pairwise
balanced design. The -recoverability performance is specified as a
simple function of the parameters of the design. To obtain our asymptotic
existence result we prove new results on the existence of pairwise balanced
designs in which the numbers of blocks of each size are specified.Comment: 15 pages, no figures. Minor improvements and updates in February 201
When is a network epidemic hard to eliminate?
We consider the propagation of a contagion process (epidemic) on a network
and study the problem of dynamically allocating a fixed curing budget to the
nodes of the graph, at each time instant. For bounded degree graphs, we provide
a lower bound on the expected time to extinction under any such dynamic
allocation policy, in terms of a combinatorial quantity that we call the
resistance of the set of initially infected nodes, the available budget, and
the number of nodes n. Specifically, we consider the case of bounded degree
graphs, with the resistance growing linearly in n. We show that if the curing
budget is less than a certain multiple of the resistance, then the expected
time to extinction grows exponentially with n. As a corollary, if all nodes are
initially infected and the CutWidth of the graph grows linearly, while the
curing budget is less than a certain multiple of the CutWidth, then the
expected time to extinction grows exponentially in n. The combination of the
latter with our prior work establishes a fairly sharp phase transition on the
expected time to extinction (sub-linear versus exponential) based on the
relation between the CutWidth and the curing budget
Almost Lossless Analog Signal Separation
We propose an information-theoretic framework for analog signal separation.
Specifically, we consider the problem of recovering two analog signals from a
noiseless sum of linear measurements of the signals. Our framework is inspired
by the groundbreaking work of Wu and Verd\'u (2010) on almost lossless analog
compression. The main results of the present paper are a general achievability
bound for the compression rate in the analog signal separation problem, an
exact expression for the optimal compression rate in the case of signals that
have mixed discrete-continuous distributions, and a new technique for showing
that the intersection of generic subspaces with subsets of sufficiently small
Minkowski dimension is empty. This technique can also be applied to obtain a
simplified proof of a key result in Wu and Verd\'u (2010).Comment: To be presented at IEEE Int. Symp. Inf. Theory 2013, Istanbul, Turke
The Ergodic Capacity of Phase-Fading Interference Networks
We identify the role of equal strength interference links as bottlenecks on
the ergodic sum capacity of a user phase-fading interference network, i.e.,
an interference network where the fading process is restricted primarily to
independent and uniform phase variations while the channel magnitudes are held
fixed across time. It is shown that even though there are cross-links,
only about disjoint and equal strength interference links suffice to
determine the capacity of the network regardless of the strengths of the rest
of the cross channels. This scenario is called a \emph{minimal bottleneck
state}. It is shown that ergodic interference alignment is capacity optimal for
a network in a minimal bottleneck state. The results are applied to large
networks. It is shown that large networks are close to bottleneck states with a
high probability, so that ergodic interference alignment is close to optimal
for large networks. Limitations of the notion of bottleneck states are also
highlighted for channels where both the phase and the magnitudes vary with
time. It is shown through an example that for these channels, joint coding
across different bottleneck states makes it possible to circumvent the capacity
bottlenecks.Comment: 19 page
- âŠ