Semi-Quantitative Group Testing

TL;DR

This paper introduces semi-quantitative group testing (SQGT), a non-binary pooling method inspired by genome sequencing, and analyzes its capacity, code constructions, and decoding algorithms using information theory.

Contribution

The paper proposes SQGT, defines its capacity, introduces SQ-disjunct codes, and provides explicit and probabilistic constructions with decoding algorithms.

Findings

Capacity bounds for SQGT are derived.

Explicit and probabilistic code constructions are provided.

Decoding algorithms for SQ-disjunct codes are developed.

Abstract

We consider a novel group testing procedure, termed semi-quantitative group testing, motivated by a class of problems arising in genome sequence processing. Semi-quantitative group testing (SQGT) is a non-binary pooling scheme that may be viewed as a combination of an adder model followed by a quantizer. For the new testing scheme we define the capacity and evaluate the capacity for some special choices of parameters using information theoretic methods. We also define a new class of disjunct codes suitable for SQGT, termed SQ-disjunct codes. We also provide both explicit and probabilistic code construction methods for SQGT with simple decoding algorithms.