Noise-Tolerant Codebooks for Semi-Quantitative Group Testing: Application to Spatial Genomics

TL;DR

This paper introduces $mbda$-ADD codes for semi-quantitative group testing in spatial genomics, providing explicit constructions and bounds that improve understanding of code rates under various distance conditions.

Contribution

It proposes a new class of codes, $mbda$-ADD, with explicit constructions and bounds for semi-quantitative group testing applications in spatial genomics.

Findings

Explicit code constructions with rates close to 1/2 for constant distance

A GV-type lower bound for codes with distance proportional to n

Upper bounds for the proposed codes

Abstract

Motivated by applications in spatial genomics, we revisit group testing (Dorfman~1943) and propose the class of $\lambda$-{\sf ADD}-codes, studying such codes with certain distance $d$ and codelength $n$. When $d$ is constant, we provide explicit code constructions with rates close to $1/2$. When $d$ is proportional to $n$, we provide a GV-type lower bound whose rates are efficiently computable. Upper bounds for such codes are also studied.