Group Testing-Based Spectrum Hole Search for Cognitive Radios

Sharma, Abhay; Murthy, Chandra R.

doi:10.1109/tvt.2014.2305978

Cited by 21 publications

(10 citation statements)

References 24 publications

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“…Cognitive radios A related communication scenario is that of cognitive radio networks, where 'secondary users' can opportunistically transmit on frequency bands which are unoccupied by primary users. We can scan combinations of several bands at the same time and detect if any signal is being transmitted across any of them, and use procedures based on group testing to determine which bands are unoccupied -see for example [16,176].…”

Section: Commmunicationsmentioning

confidence: 99%

Group Testing: An Information Theory Perspective

Aldridge¹,

Johnson²,

Scarlett³

2019

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The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. This is a sparse inference problem with a combinatorial flavour, with applications in medical testing, biology, telecommunications, information technology, data science, and more.In this monograph, we survey recent developments in the group testing problem from an information-theoretic perspective. We cover several related developments: efficient algorithms with practical storage and computation requirements, achievability bounds for optimal decoding methods, and algorithmindependent converse bounds. We assess the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the rate of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, we identify several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement.In addition, we survey results concerning a number of variations on the standard group testing problem, including partial recovery criteria, adaptive algorithms with a limited number of stages, constrained test designs, and sublineartime algorithms.S 0 , S 1 partition of the defective set (Equation (4.4)) ı information density (Equation (4.6)) X 0,τ , X 1,τ sub-matrices of X corresponding to (S 0 , S 1 ) with |S 0 | = τ (Equation (4.14))τ ) (Equation (4.16)) 2. If the preceding test is negative, A contains no defective items, and we halt. If the test is positive, continue. 3. If A consists of a single item, then that item is defective, and we halt. Otherwise, pick half of the items in A, and call this set B. Perform a single test of the pool B. 4. If the test is positive, set A := B. If the test is negative, set A := A \ B. Return to Step 3. A BRIEF REVIEW OF ZERO-ERROR GROUP TESTINGObserve that S(i) is the set of tests containing item i, while S(K) is the set of positive tests when the defective set is K.Definition 1.10. A matrix X is called k-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| = k.A matrix X is calledk-separable if the support unions S(L) are distinct over all subsets L ⊆ {1, 2, . . . , n} of size |L| ≤ k.Clearly, using a k-separable matrix as a test design ensures that group testing will provide different outcomes for each possible defective set of size k; thus,

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Section: Commmunicationsmentioning

confidence: 99%

Group Testing: An Information Theory Perspective

Aldridge¹,

Johnson²,

Scarlett³

2019

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“…Also, we initialize the messages from item nodes to their neighboring test nodes as in (2). After that, for each iteration j ≥ 1, when we want to update the messages from tests to items, we randomly choose a test node and only send messages from that test node to its neighbouring item nodes.…”

Section: B Random Scheduling Belief Propagationmentioning

confidence: 99%

“…Aside from the theoretical endeavors, the GT problem has also gained substantial attention from the practical perspective. In particular, the GT problem has been studied for a wide range of applications from biology and medicine [1] to information and communication technology [2], [3], and computer science [4]. Very recently, group testing has also been used for COVID-19 detection [5]- [8].…”

Section: Introductionmentioning

confidence: 99%

Scheduling Improves the Performance of Belief Propagation for Noisy Group Testing

Karimi¹,

Heidarzadeh²,

Narayanan³

et al. 2021

Preprint

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This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of this work is on the practical settings with a limited number of items rather than the asymptotic regime. In the current literature, belief propagation has been shown to be effective in recovering defective items from the test results. In this work, we adopt two variants of the belief propagation algorithm for the noisy group testing problem. These algorithms have been used successfully in decoding of low-density parity-check codes. We perform an experimental study and using extensive simulations we show that these algorithms achieve higher success probability, lower false-negative and false-positive rates compared to the traditional belief propagation algorithm. For instance, our results show that the proposed algorithms can reduce the false-negative rate by about 50% (or more) when compared to the traditional BP algorithm, under the combinatorial model. Moreover, under the probabilistic model, this reduction in falsenegative rate increases to about 80% for the tested cases.

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“…When m < k, although support recovery is still possible as we show in this work, data recovery is no longer possible, since there are infinitely many solutions even after restricting to the support. Recovery of the support, rather than the data vectors, is important in several practical applications including spectrum sensing [26] and group testing [33].…”

Section: Introductionmentioning

confidence: 99%

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

Ramesh

Murthy

Tyagi

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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Data samples from Ê d with a common support of size k are accessed through m random linear projections per sample. It is well-known that roughly k measurements from a single sample are sufficient to recover the support. In the multiple sample setting, do k overall measurements still suffice when only m < k measurements per sample are allowed? We answer this question in the negative by considering a generative model setting with independent samples drawn from a subgaussian prior. We show that n = Θ((k 2 /m 2 ) · log k(d − k)) samples are necessary and sufficient to recover the support exactly. In turn, this shows that k overall samples are insufficient for support recovery when m < k; instead we need about k 2 /m overall measurements. Our proposed sample-optimal estimator has a closed-form expression, has computational complexity of O(dnm), and is of independent interest.

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Group Testing-Based Spectrum Hole Search for Cognitive Radios

Cited by 21 publications

References 24 publications

Group Testing: An Information Theory Perspective

Group Testing: An Information Theory Perspective

Scheduling Improves the Performance of Belief Propagation for Noisy Group Testing

Sample-Measurement Tradeoff in Support Recovery Under a Subgaussian Prior

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