Group testing for non-uniformly quantized adder channels

We present a new family of codes for non-uniformly quantized adder channels. Quantized adder channels are generalizations of group testing models, which were studied under the name of semi-quantitative group testing. We describe non-binary group testing schemes in which the test matrices are generated by concatenating scaled disjunct codebooks, with the scaling parameters determined through lexicographical ordering constraints. In addition, we propose simple iterative decoding methods for one class of such codes.