183 research outputs found
Adaptive group testing as channel coding with feedback
Group testing is the combinatorial problem of identifying the defective items
in a population by grouping items into test pools. Recently, nonadaptive group
testing - where all the test pools must be decided on at the start - has been
studied from an information theory point of view. Using techniques from channel
coding, upper and lower bounds have been given on the number of tests required
to accurately recover the defective set, even when the test outcomes can be
noisy.
In this paper, we give the first information theoretic result on adaptive
group testing - where the outcome of previous tests can influence the makeup of
future tests. We show that adaptive testing does not help much, as the number
of tests required obeys the same lower bound as nonadaptive testing. Our proof
uses similar techniques to the proof that feedback does not improve channel
capacity.Comment: 4 pages, 1 figur
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
Delay-rate tradeoff in ergodic interference alignment
Ergodic interference alignment, as introduced by Nazer et al (NGJV), is a
technique that allows high-rate communication in n-user interference networks
with fast fading. It works by splitting communication across a pair of fading
matrices. However, it comes with the overhead of a long time delay until
matchable matrices occur: the delay is q^n^2 for field size q.
In this paper, we outline two new families of schemes, called JAP and JAP-B,
that reduce the expected delay, sometimes at the cost of a reduction in rate
from the NGJV scheme. In particular, we give examples of good schemes for
networks with few users, and show that in large n-user networks, the delay
scales like q^T, where T is quadratic in n for a constant per-user rate and T
is constant for a constant sum-rate. We also show that half the single-user
rate can be achieved while reducing NGJV's delay from q^n^2 to q^(n-1)(n-2).
This extended version includes complete proofs and more details of good
schemes for small n.Comment: Extended version of a paper presented at the 2012 International
Symposium on Information Theory. 7 pages, 1 figur
The Capacity of Adaptive Group Testing
We define capacity for group testing problems and deduce bounds for the
capacity of a variety of noisy models, based on the capacity of equivalent
noisy communication channels. For noiseless adaptive group testing we prove an
information-theoretic lower bound which tightens a bound of Chan et al. This
can be combined with a performance analysis of a version of Hwang's adaptive
group testing algorithm, in order to deduce the capacity of noiseless and
erasure group testing models.Comment: 5 page
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
On the optimality of some group testing algorithms
We consider Bernoulli nonadaptive group testing with k=Θ(n^θ) defectives, for θ∈(0,1). The practical definite defectives (DD) detection algorithm is known to be optimal for θ≥1/2. We give a new upper bound on the rate of DD, showing that DD is strictly suboptimal for θ<0.41. We also show that the SCOMP algorithm and algorithms based on linear programming achieve a rate at least as high as DD, so in particular are also optimal for θ≥1/2
A Finite State Machine Approach to Cluster Identification Using the Hoshen-Kopelman Algorithm
The purpose of this study was to develop an efficient finite state machine implementation of the eponymous Hoshen-Kopelman cluster identification algorithm using the nearest-eight neighborhood rule suitable to applications such as computer modeling for landscape ecology. The implementation presented in this study was tested using both actual land cover maps, as well as randomly generated data similar to those in the original presentation of the Hoshen-Kopelman algorithm for percolation analysis. The finite state machine implementation clearly outperformed a straightforward adaptation of the original Hoshen-Kopelman algorithm on either data type. Research was also conducted to explore the finite state machine\u27s performance on a Palm mobile computing device, and while it was competitive, it did not exceed the performance of the straightforward Hoshen-Kopelman implementation. However, a discussion of why this was the case is provided along with a possible remedy for future hardware designs
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