Low-Density Parity-Check Codes and Spatial Coupling for Quantitative Group Testing
arxiv(2024)
摘要
A non-adaptive quantitative group testing (GT) scheme based on sparse
codes-on-graphs in combination with low-complexity peeling decoding was
introduced and analyzed by Karimi et al.. In this work, we propose a variant of
this scheme based on low-density parity-check codes where the BCH codes at the
constraint nodes are replaced by simple single parity-check codes. Furthermore,
we apply spatial coupling to both GT schemes, perform a density evolution
analysis, and compare their performance with and without coupling. Our analysis
shows that both schemes improve with increasing coupling memory, and for all
considered cases, it is observed that the LDPC code-based scheme substantially
outperforms the original scheme. Simulation results for finite block length
confirm the asymptotic density evolution thresholds.
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