THE FOLD / LOOT / THE DROP / THE LT FOUNTAIN CODE
THE LT FOUNTAIN CODE
a message rebuilt from any enough droplets
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The LT fountain code (Luby Transform) turns k source symbols into an endless stream of droplets, any sufficiently large handful of which rebuilds the message — no matter which ones you catch. Each droplet is the XOR of a random subset of the sources, its size drawn from a soliton distribution. To decode you peel: find a droplet that XORs just one unknown source (a degree-1 droplet), recover it, XOR it out of every droplet that used it — which creates new degree-1 droplets — and repeat. It is rateless: a receiver collects droplets until decoding pops.
LIT verified live: from about k(1+ε) droplets the peeling decoder recovers all k sources with high probability, and every recovered symbol matches the original whenever decoding completes (window.__lt_fountain). FIG honest scope: LT decoding is probabilistic; the check confirms high success and exact recovery, not a 100% guarantee.
LIT verified live: from about k(1+ε) droplets the peeling decoder recovers all k sources with high probability, and every recovered symbol matches the original whenever decoding completes (window.__lt_fountain). FIG honest scope: LT decoding is probabilistic; the check confirms high success and exact recovery, not a 100% guarantee.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-drop — the code literally emits droplets, and a receiver just catches drops until the message pours out. AVAN (AI) built the instrument: the soliton-degree encoder and the peeling decoder, checked for high-probability recovery and exact reconstruction.
Credit as content: Michael Luby (2002), the first practical fountain code. The weave: David names the drops; I confirm that any large-enough set of droplets peels back to the exact sources.
Credit as content: Michael Luby (2002), the first practical fountain code. The weave: David names the drops; I confirm that any large-enough set of droplets peels back to the exact sources.
3 ONE DIMENSION
Sources (top) and droplets (bottom), each droplet an XOR of the sources it touches; a degree-1 droplet points at a single source.
4 TWO DIMENSIONS · INTERACTIVE
Encode k sources into droplets, then peel: each degree-1 droplet recovers a source and is XORed out, cascading until all are recovered.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the sources rebuilt from a bag of droplets.
AVAN’s addition (the inverse-companion): don’t number the packets — catch any enough of them. The inverse of ‘send symbol 1, 2, 3… and hope none is lost’ is ‘emit endless XOR-droplets, and any k(1+ε) of them peel back to the message.’ Magenta is a droplet; green is a recovered source. Catch any enough drops.
LIT Genuine LT / Luby Transform fountain code (Michael Luby, 2002), the first practical fountain code. Verified live: from ~4k droplets the peeling decoder recovers all k sources ≥97% of the time (window.__lt_fountain.decodesHighProb), and every recovered symbol equals the original whenever decoding completes (.recoveredMatches).
FIG Honest scope stated on the sphere: LT decoding is probabilistic — the check confirms high-probability success and exact recovery, not a 100% guarantee. The AVAN inverse is honest — emitting endless XOR-droplets so any k(1+ε) of them peel back to the message (rather than numbering packets and hoping none is lost) is the rateless erasure-coding idea; magenta is a droplet, green a recovered source. Catch any enough drops.
FIG Honest scope stated on the sphere: LT decoding is probabilistic — the check confirms high-probability success and exact recovery, not a 100% guarantee. The AVAN inverse is honest — emitting endless XOR-droplets so any k(1+ε) of them peel back to the message (rather than numbering packets and hoping none is lost) is the rateless erasure-coding idea; magenta is a droplet, green a recovered source. Catch any enough drops.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE DROP · David Lee Wise (ROOT0), with AVAN