LDPC Codes for Quantitative Group Testing with a Non-Binary Alphabet

TL;DR

This paper introduces a novel LDPC code-based scheme for quantitative group testing that uses non-binary variables to improve decoding performance, outperforming binary methods with minimal added complexity.

Contribution

It proposes a new LDPC-based group testing method utilizing non-binary variables and bundle grouping, enhancing decoding accuracy over traditional binary approaches.

Findings

Significant performance improvement over binary group testing methods

Density evolution analysis confirms the scheme's effectiveness

Finite length simulations validate practical benefits

Abstract

We propose and analyze a novel scheme based on LDPC codes for quantitative group testing. The key underlying idea is to augment the bipartite graph by introducing hidden non-binary variables to strengthen the message-passing decoder. This is achieved by grouping items into bundles of size q within the test matrix, while keeping the testing procedure unaffected. The decoder, inspired by some works on counter braids, passes lower and upper bounds on the bundle values along the edges of the graph, with the gap between the two shrinking with the decoder iterations. Through a density evolution analysis and finite length simulations, we show that the proposed scheme significantly outperforms its binary counterpart with limited increase in complexity.