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

Mashauri, Mgeni Makambi LU ; i Amat, Alexandre Graell and Lentmaier, Michael LU (2025) In IEEE Communications Letters 29(3). p.630-634
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 (DE) analysis and finite length simulations, we show that the proposed scheme significantly outperforms its binary counterpart with limited increase... (More)

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 (DE) analysis and finite length simulations, we show that the proposed scheme significantly outperforms its binary counterpart with limited increase in complexity.

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Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
codes-on-graphs, LDPC codes, message passing, non-binary variables, quantitative group testing
in
IEEE Communications Letters
volume
29
issue
3
pages
5 pages
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • scopus:86000800209
ISSN
1089-7798
DOI
10.1109/LCOMM.2025.3538910
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 IEEE. All rights reserved.
id
38d5d547-85ca-4e2a-802b-b3cd2e449be6
date added to LUP
2025-06-23 15:41:54
date last changed
2025-06-23 15:42:59
@article{38d5d547-85ca-4e2a-802b-b3cd2e449be6,
  abstract     = {{<p>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 (DE) analysis and finite length simulations, we show that the proposed scheme significantly outperforms its binary counterpart with limited increase in complexity.</p>}},
  author       = {{Mashauri, Mgeni Makambi and i Amat, Alexandre Graell and Lentmaier, Michael}},
  issn         = {{1089-7798}},
  keywords     = {{codes-on-graphs; LDPC codes; message passing; non-binary variables; quantitative group testing}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{630--634}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  series       = {{IEEE Communications Letters}},
  title        = {{LDPC Codes for Quantitative Group Testing With a Non-Binary Alphabet}},
  url          = {{http://dx.doi.org/10.1109/LCOMM.2025.3538910}},
  doi          = {{10.1109/LCOMM.2025.3538910}},
  volume       = {{29}},
  year         = {{2025}},
}