Fundamental Limits of Non-Adaptive Group Testing with Markovian Correlation

TL;DR

This paper analyzes the fundamental limits of non-adaptive group testing when items are infected according to a Markov chain, proposing an efficient testing strategy that nearly reaches the theoretical entropy bound in a sparse infection regime.

Contribution

It introduces a non-adaptive testing method for Markovian correlated infections that is nearly optimal and quantifies the benefits of exploiting correlation.

Findings

Tests reduce as expected burst length increases.

Achieves asymptotically vanishing error with near-optimal number of tests.

Performance parallels independent group testing setting.

Abstract

We study a correlated group testing model where items are infected according to a Markov chain, which creates bursty binfection patterns. Focusing on a very sparse infections regime, we propose a non adaptive testing strategy with an efficient decoding scheme that is nearly optimal. Specifically, it achieves asymptotically vanishing error with a number of tests that is within a $1/\ln(2) \approx 1.44$ multiplicative factor of the fundamental entropy bound a result that parallels the independent group testing setting. We show that the number of tests reduces with an increase in the expected burst length of infected items, quantifying the advantage of exploiting correlation in test design.