Improved encoding and decoding for non-adaptive threshold group testing
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The goal of threshold group testing is to identify up to d defective items among a population of n items, where d is usually much smaller than n. A test is positive if it has at least u defective items and negative otherwise. Our objective is to identify defective items in sublinear time the number of items, e.g., poly(d, n), by using the number of tests as low as possible. In this paper, we reduce the number of tests to O ( h ×d^2 ^2n/W^2(d n)) and the decoding time to O ( dec_0 × h ), where mathrmdec_0 = O ( d^3.57^6.26n/W^6.26(d n)) + O ( d^6 ^4n/W^4(d n)), h = O( d_0^2 n/d_0/(1-p)^2) , d_0 = {u, d - u }, p ∈ [0, 1), and W(x) = Θ( x - x). If the number of tests is increased to O( h ×d^2^3n/W^2(d n)), the decoding complexity is reduced to O (dec_1 × h ), where dec_1 = {d^2 ^3n/W^2(d n), ud ^4n/W^3(d n)}. Moreover, our proposed scheme is capable of handling errors in test outcomes.
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