Raptor codes

Raptor codes are a class of fountain codes that can be viewed as a serial concatenation of a forward error correction code and a LT code.

Let $\mathcal{C}$ be a linear code of block length $n$ and dimension $k$, and let $\Omega(x)$ be a degree distribution. A Raptor code with parameters $(k, \mathcal{C}, \Omega(x))$ is an LT-code with distribution on symbols which are the coordinates of codewords in \mathcal{C}. The code \mathcal{C} is called the pre-code of the Raptor code. The input symbols of a Raptor code are the symbols used to construct the codeword in consisting of intermediate symbols. The output symbols are the symbols generated by the LT-code from the intermediate symbols. Typically,we assume that \mathcal{C} is equipped with a systematic encoding, though this is not necessary.