Rateless erasure coding via CRT decomposition. The ring IS the code. CC0. No patents. No Luby transform.
Traditional fountain codes (LT, Raptor) use complex XOR-graph constructions patented by Qualcomm.
CRT fountain codes use the ring structure itself. No special encoding needed.
Encode:
1. Each data symbol lives in Z/970200Z
2. CRT decomposes it into 5 independent channels:
n -> (n mod 8, n mod 9, n mod 25, n mod 49, n mod 11)
3. Each channel residue = one "drop" in the fountain
4. Generate drops forever: cycle through channels, add redundancy
Decode:
1. Collect drops (channel residues) over lossy channel
2. For each data symbol, track which channels received
3. When all 5 channels arrive: CRT reconstruct -> original symbol
4. L=11 channel: error detection for FREE
The joke: there IS no encoding algorithm. CRT IS the code.
Qualcomm patented complex graph structures. We just decompose numbers.
Each row = one data symbol. Columns = 5 CRT channels. Green = received. Dark = lost. Cyan = decoded.
CRT fountain vs naive repetition. Partial recovery + error correction = structural advantage.
Corrupt one channel residue. L=11 detects the inconsistency. CRT redundancy corrects it.