Symmetric Group Testing and Superimposed Codes

TL;DR

This paper introduces symmetric group testing, a generalization of classical group testing with a ternary output alphabet and symmetric input roles, providing theoretical bounds and code constructions.

Contribution

It extends disjunct and separable codes to symmetric group testing, deriving bounds and construction methods using probabilistic and coding theoretic techniques.

Findings

Derived necessary and sufficient conditions for test numbers in noise-free and noisy cases.

Extended disjunct and separable codes to symmetric group testing.

Provided bounds and construction methods for new code families.

Abstract

We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a ternary alphabet. Using an information-theoretic approach, we derive sufficient and necessary conditions for the number of tests required for noise-free and noisy reconstructions. Furthermore, we extend the notion of disjunct (zero-false-drop) and separable (uniquely decipherable) codes to the case of symmetric group testing. For the new family of codes, we derive bounds on their size based on probabilistic methods, and provide construction methods based on coding theoretic ideas.