The Journal of Korea Institute of Information, Electronics, and Communication Technology (한국정보전자통신기술학회논문지)

Korea Information Electronic Communication Technology (한국정보전자통신기술학회)
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Maximum Product Detection Algorithm for Group Testing Frameworks

  • Seong, Jin-Taek (Department of Convergence Software, Mokpo National University)
  • Received : 2020.04.03
  • Accepted : 2020.04.14
  • Published : 2020.04.30
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Abstract

In this paper, we consider a group testing (GT) framework which is to find a set of defective samples out of a large number of samples. To handle this framework, we propose a maximum product detection algorithm (MPDA) which is based on maximum a posteriori probability (MAP). The key idea of this algorithm exploits iterative detection to propagate belief to neighbor samples by exchanging marginal probabilities between samples and output results. The belief propagation algorithm as a conventional approach has been used to detect defective samples, but it has computational complexity to obtain the marginal probability in the output nodes which combine other marginal probabilities from the sample nodes. We show that the our proposed MPDA provides a benefit to reduce computational complexity up to 12% in runtime, while its performance is only slightly degraded compared to the belief propagation algorithm. And we verify the simulations to compare the difference of performance.

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References

  1. R. Dorfman, "The Detection of Defective Members of Large Populations," The Annals of Mathematical Statistics, vol. 14, no. 4, pp. 436-440, Dec. 1943. https://doi.org/10.1214/aoms/1177731363
  2. D.-Z. Du and F.K. Hwang, Pooling Designs and Nonadaptive Group Testing: Important Tools for DNA Sequencing, World Scientific, 2006.
  3. C.L. Chan, P.H. Che, S. Jaggi, and V. Saligrama, "Non-adaptive probabilistic group testing with noisy measurements: near-optimal bounds with efficient algorithms," 49th Annual Allerton Conference on Communication, Control, and Computing, pp. 1832-1839. Sep. 2011.
  4. M. Aldridge, L. Baldassini, and O. Johnson, "Group Testing Algorithms: Bounds and Simulations," IEEE Transactions on Information Theory, vol. 60, no. 6, pp. 3671-3687, Jun. 2014. https://doi.org/10.1109/TIT.2014.2314472
  5. L. Baldassini, O. Johnson, M. Aldridge, "The capacity of adaptive group testing," IEEE International Symposium on Information Theory, pp. 2676-2680, Oct. 2013.
  6. G.K. Atia and V. Saligrama, "Boolean Compressed Sensing and Noisy Group Testing," IEEE Transactions on Information Theory, vol. 58, no. 3, pp. 1880-1901. Mar. 2012. https://doi.org/10.1109/TIT.2011.2178156
  7. J. Scarlett, "Noisy Adaptive Group Testing: Bounds and Algorithms," IEEE Transactions on Information Theory, vol. 65, no. 6, pp. 3646-3661. Jun. 2019. https://doi.org/10.1109/TIT.2018.2883604
  8. M.C. Davey and D. Mackey, "Low-density parity-check codes over GF(q)," IEEE Communications Letters, vol. 2, no. 6, pp. 165-167, Jun. 1998. https://doi.org/10.1109/4234.681360
  9. J.-T. Seong, "A New Upper Bound for Finding Defective Samples in Group Testing," IEICE Transactions on Information and Systems, advance publication, Feb. 2020.