LDPC Codes for Quantitative Group Testing with a Non-Binary Alphabet
Mgeni Makambi Mashauri, Alexandre Graell i Amat, Michael Lentmaier

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSARS-CoV-2 detection and testing · Advanced biosensing and bioanalysis techniques · Biosensors and Analytical Detection
