Fountain codes
Fountain codes are record-breaking sparse-graph codes for channels with erasures, such as the internet, where files are transmitted in multiple small packets, each of which is either received without error or not received. Standard file transfer protocols simply chop a file up into K packet-sized pieces, then repeatedly transmit each packet until it is successfully received. A back channel is required for the transmitter to find out which packets need retransmitting. In contrast, fountain codes make packets that are random functions of the whole file. The transmitter sprays packets at the receiver without any knowledge of which packets are received. Once the receiver has received any N packets, where N is just slightly greater than the original file size K, the whole file can be recovered. In the paper random linear fountain codes, LT codes, and raptor codes are reviewed. The computational costs of the best fountain codes are astonishingly small, scaling linearly with the file size.
