Low-Density Parity-Check Codes and Spatial Coupling for Quantitative Group Testing

Explore a 35-minute lecture on low-density parity-check codes and spatial coupling for quantitative group testing. Delve into an innovative non-adaptive quantitative group testing scheme based on sparse codes-on-graphs and low-complexity peeling decoding. Discover a proposed variant using low-density parity-check codes, replacing BCH codes with single parity-check codes at constraint nodes. Examine the application of spatial coupling to both group testing schemes and compare their performance through density evolution analysis. Learn how increasing coupling memory improves both schemes, with the LDPC code-based approach significantly outperforming the original. Gain insights into finite block length simulation results that confirm asymptotic density evolution thresholds in this talk by Michael Lentmaier from Lund University, part of the Application-Driven Coding Theory series at the Simons Institute.