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.

翻译：我们提出并分析了一种基于LDPC码的定量群组测试新方案。其核心思想是通过引入隐藏的非二进制变量来增强二分图的消息传递解码器。这是通过在测试矩阵中将项目分组为大小为q的束来实现的，同时保持测试过程不受影响。受计数器编织相关研究的启发，该解码器沿着图的边传递束值的下界和上界，两者之间的差距随着解码器迭代次数的增加而缩小。通过密度进化分析和有限长度仿真，我们证明所提出的方案在复杂度增加有限的情况下，性能显著优于其二进制对应方案。