  In this paper, we consider the group testing problem with adaptive test
designs and noisy outcomes. We propose a computationally efficient four-stage
procedure with components including random binning, identification of bins
containing defective items, 1-sparse recovery via channel codes, and a
"clean-up" step to correct any errors from the earlier stages. We prove that
the asymptotic required number of tests comes very close to the best known
information-theoretic achievability bound (which is based on computationally
intractable decoding), and approaches a capacity-based converse bound in the
low-sparsity regime.
