Computer Science – Information Theory
Scientific paper
2010-10-12
Computer Science
Information Theory
5 pages, 3 figures, presented at the Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing, Septemb
Scientific paper
10.1109/ALLERTON.2010.5707018
An information theoretic perspective on group testing problems has recently been proposed by Atia and Saligrama, in order to characterise the optimal number of tests. Their results hold in the noiseless case, where only false positives occur, and where only false negatives occur. We extend their results to a model containing both false positives and false negatives, developing simple information theoretic bounds on the number of tests required. Based on these bounds, we obtain an improved order of convergence in the case of false negatives only. Since these results are based on (computationally infeasible) joint typicality decoding, we propose a belief propagation algorithm for the detection of defective items and compare its actual performance to the theoretical bounds.
Johnson Oliver
Sejdinovic Dino
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