Low-Density Parity-Check codes - capacity-approaching performance
Sparse Matrix: H has very few 1s (low density). This enables efficient message-passing decoding!
Tanner Graph: Bipartite graph with variable nodes (bits) and check nodes (parity equations). Messages pass along edges.
Belief Propagation: Iteratively update beliefs about each bit based on parity check constraints.
Performance: Can achieve within 0.0045 dB of Shannon limit! Even better than Turbo codes for long blocks.
Applications: Wi-Fi 6 (802.11ax), 5G NR, DVB-S2, 10GBase-T Ethernet, SSD storage.