Tuesday, July 9, 2013

Damn Cool Algorithms: Fountain Codes

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That's right, it's time for another episode of the frustratingly infrequent Damn Cool Algorithms series! If you're not familiar with it, you might want to check out some of the previous posts.

Today's subject is Fountain Codes, otherwise known as "rateless codes". A fountain code is a way to take some data - a file, for example - and transform it into an effectively unlimited number of encoded chunks, such that you can reassemble the original file given any subset of those chunks, as long as you have a little more than the size of the original file. In other words, it lets you create a 'fountain' of encoded data; a receiver can reassemble the file by catching enough 'droplets', regardless of which ones they get and which ones they miss.

What makes this so remarkable is that it allows you to send a file over a lossy connection - such as, say, the internet - in a way that doesn't rely on you knowing the rate of packet loss, and doesn't require the receivers to communicate anything back to you about which packets they missed. You can see how this would be useful in a number of situations, from sending a static file over a broadcast medium, such as on-demand TV, to propagating chunks of a file amongst a large number of peers, like BitTorrent does.

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