SAFFRON: A Fast, Efficient, and Robust Framework for Group Testing Based on Sparse-Graph Codes

Group testing is the problem of identifying <inline-formula><tex-math notation="LaTeX">K</tex-math></inline-formula> defective items among <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> items by pooling gro...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 67; no. 17; pp. 4649 - 4664
Main Authors: Lee, Kangwook, Chandrasekher, Kabir, Pedarsani, Ramtin, Ramchandran, Kannan
Format: Journal Article
Language:English
Published: New York IEEE 01.09.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation algorithms
Complexity
Complexity theory
compressed sensing
Decoding
Group testing
Noise measurement
Offsets
Saffron
Signal processing algorithms
sparse-graph codes
sub-linear decoding complexity
Testing
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Group testing is the problem of identifying <inline-formula><tex-math notation="LaTeX">K</tex-math></inline-formula> defective items among <inline-formula><tex-math notation="LaTeX">n</tex-math></inline-formula> items by pooling groups of items. In this paper, we design group testing algorithms for approximate recovery with order-optimal sample complexity by leveraging design and analysis tools from modern sparse-graph coding theory. Our algorithm, SAFFRON, recovers at least <inline-formula><tex-math notation="LaTeX">(1-\varepsilon)K</tex-math></inline-formula> defective items w.p. <inline-formula><tex-math notation="LaTeX">1-K/n^r</tex-math></inline-formula> with <inline-formula><tex-math notation="LaTeX">m=2(1+r)C(\varepsilon)K\log _2{n}</tex-math></inline-formula> tests, where <inline-formula><tex-math notation="LaTeX">\varepsilon</tex-math></inline-formula> is an arbitrarily small constant, <inline-formula><tex-math notation="LaTeX">C(\varepsilon)</tex-math></inline-formula> is a precisely characterizable constant, and <inline-formula><tex-math notation="LaTeX">r</tex-math></inline-formula> is any positive integer. The decoding complexity is <inline-formula><tex-math notation="LaTeX">\Theta (K\log n)</tex-math></inline-formula>. We also propose variations of SAFFRON, which are robust to noise and unknown offsets. For example, for <inline-formula><tex-math notation="LaTeX">n \simeq 4.3\times 10^9</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">K = 128</tex-math></inline-formula>, our algorithm is observed to recover all defective items with <inline-formula><tex-math notation="LaTeX">m \simeq 8.3\times 10^{5}</tex-math></inline-formula> tests, even in the presence of noisy test results. Moreover, the decoding time takes less than 4 seconds on a laptop with a 2 GHz Intel Core i7 and 8 GB memory.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2019.2929938