Matthew Aldridge

Group Testing Algorithms: Bounds and Simulations

We consider the problem of nonadaptive noiseless group testing of N items of which K are defective. We describe four detection algorithms, the COMP algorithm of Chan et al., two new algorithms, DD and SCOMP, which require stronger evidence to declare an item defective, and an essentially optimal but computationally difficult algorithm called SSS. We consider an important class of designs for the group testing problem, namely those in which the test structure is given via a Bernoulli random process. In this class of Bernoulli designs, by considering the asymptotic rate of these algorithms, we show that DD outperforms COMP, that DD is essentially optimal in regimes where K ≥ √N, and that no algorithm can perform as well as the best nonrandom adaptive algorithms when K > N0.35. In simulations, we see that DD and SCOMP far outperform COMP, with SCOMP very close to the optimal SSS, especially in cases with larger K.

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 Hwangs adaptive group testing algorithm, in order to deduce the capacity of noiseless and erasure group testing models.

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 qn2 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 qT, 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 NGJVs delay from qn2 to q(n-1)(n-2).

Almost separable matrices

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The Capacity of Bernoulli Nonadaptive Group Testing

m\times n

On the optimality of some group testing algorithms

m×n matrix

Interference Mitigation in Large Random Wireless Networks

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