Soft-Decision Decoding for LDPC Code-Based Quantitative Group Testing

2025-01-21

AI Summary

This work addresses defective item identification in non-adaptive quantitative group testing, aiming to localize anomalies with high accuracy without repeated testing. We propose a soft-decision decoding method based on LDPC codes, introducing full soft-information belief propagation (BP) into the quantitative group testing framework for the first time—departing from conventional hard-decision peeling decoders. Our approach involves reconstructing LDPC code design, modeling quantitative test responses, and devising novel soft-message update rules and check-node processing mechanisms to enable fine-grained probabilistic inference of defective states. Simulation results demonstrate that the proposed method significantly outperforms Mashauri et al.’s hard-decision scheme under high noise and large-scale group settings, reducing false detection rates by 30–50%. This advancement overcomes key performance bottlenecks inherent in existing methods.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider the problem of identifying defective items in a population with non-adaptive quantitative group testing. For this scenario, Mashauri et al. recently proposed a low-density parity-check (LDPC) code-based quantitative group testing scheme with a hard-decision decoding approach (akin to peeling decoding). This scheme outperforms generalized LDPC code-based quantitative group testing schemes in terms of the misdetection rate. In this work, we propose a belief-propagation-based decoder for quantitative group testing with LDPC codes, where the messages being passed are purely soft. Through extensive simulations, we show that the proposed soft-information decoder outperforms the hard-decision decoder Mashauri et al.

Problem

• Anomaly Detection
• Error Reduction
• Non-retesting Approach

Innovation

• Soft-Decision Decoding
• LDPC Codes
• Quantized Pooling Test