Code Construction and Decoding Algorithms for Semi-Quantitative Group Testing with Nonuniform Thresholds

TL;DR

This paper introduces semi-quantitative group testing with nonuniform thresholds, defining new sequence families for code design, and presents decoding algorithms with complexity and performance analysis.

Contribution

It develops new sequence-based code structures for semi-quantitative group testing with arbitrary thresholds and efficient recursive decoding methods.

Findings

New sequence families for code design

Efficient recursive decoding algorithms

Performance analysis of decoding methods

Abstract

We analyze a new group testing scheme, termed semi-quantitative group testing, which may be viewed as a concatenation of an adder channel and a discrete quantizer. Our focus is on non-uniform quantizers with arbitrary thresholds. For the most general semi-quantitative group testing model, we define three new families of sequences capturing the constraints on the code design imposed by the choice of the thresholds. The sequences represent extensions and generalizations of Bh and certain types of super-increasing and lexicographically ordered sequences, and they lead to code structures amenable for efficient recursive decoding. We describe the decoding methods and provide an accompanying computational complexity and performance analysis.