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.