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The goal of non-adaptive group testing is to identify at most $d$ defectiveitems from $N$ items, in which a test of a subset of $N$ items is positive ifit contains at least one defective item, and negative otherwise. However, inmany cases, especially in biological screening, the outcome is unreliable dueto biochemical interaction; i.e., \textit{noise.} Consequently, a positiveresult can change to a negative one (false negative) and vice versa (falsepositive). In this work, we first consider the dilution effect in which\textit{the degree of noise depends on the number of items in the test}. Twoefficient schemes are presented for identifying the defective items in timelinearly to the number of tests needed. Experimental results validate ourtheoretical analysis. Specifically, setting the error precision of 0.001 and$d\leq16$, our proposed algorithms always identify all defective items in lessthan 7 seconds for $N=2^{33}\approx 9$ billion.

Efficient Decoding Schemes for Noisy Non-Adaptive Group Testing when Noise Depends on Number of Items in Test