X · Coding theory
Erasure codes & LDPC
What it is
Generalise RS to large block sizes with sparse parity equations. Encode/decode in linear time using belief propagation. Approach Shannon's channel-capacity limit.
Where it lives
5G, Wi-Fi 6, deep-space probes, modern distributed storage (S3, GCS).
The key insight
LDPC codes used in 5G achieve rates within 0.5 dB of theoretical capacity. The same family powers every "this satellite link works at all" engineering.