  We propose a novel group testing method, termed semi-quantitative group
testing, motivated by a class of problems arising in genome screening
experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary
pooling scheme that may be viewed as a concatenation of an adder channel and an
integer-valued quantizer. In its full generality, SQGT may be viewed as a
unifying framework for group testing, in the sense that most group testing
models are special instances of SQGT. For the new testing scheme, we define the
notion of SQ-disjunct and SQ-separable codes, representing generalizations of
classical disjunct and separable codes. We describe several combinatorial and
probabilistic constructions for such codes. While for most of these
constructions we assume that the number of defectives is much smaller than
total number of test subjects, we also consider the case in which there is no
restriction on the number of defectives and they may be as large as the total
number of subjects. For the codes constructed in this paper, we describe a
number of efficient decoding algorithms. In addition, we describe a belief
propagation decoder for sparse SQGT codes for which no other efficient decoder
is currently known. Finally, we define the notion of capacity of SQGT and
evaluate it for some special choices of parameters using information theoretic
methods.
