## Description

Raptor codes are concatenated erasure codes with two layers: an outer pre-code and a Luby-Transform (LT) inner code. The pre-code is a linear binary erasure code, which is applied first to the input to create some redundant data. The LT code is then applied to the intermediate symbols from the pre-code to generate final output symbols to be transmitted.

The parameters for a Raptor code are \( (k, C, \Omega(x)) \), with \(C\) being the pre-code with dimension \( k \), and \( \Omega(x) \) being the degree distribution for the LT code.

The times to encode and decode source blocks are both linear. The space requirement is \(1/R \), where \(R\) is the rate of the pre-code. Raptor codes with the simplest output distribution (LT code) are called pre-code-only (PCO).

## Protection

## Decoding

## Realizations

## Notes

## Parent

## Child

- Luby transform (LT) code — Raptor codes using a trivial pre-code are LT codes. Typically, Raptor codes have constant-sized more overhead but are faster to decode.

## Cousin

- Tornado code — Tornado codes, which can be used as a pre-code for raptor codes, also use a multi-layer approach where redundant symbols are created by one code for another code to use as input.

## References

- [1]
- A. Shokrollahi, “Raptor codes”, IEEE Transactions on Information Theory 52, 2551 (2006) DOI
- [2]
- Petar Maymounkov, Online codes, Technical report, New York University, 2002.
- [3]
- F. Lazaro, G. Liva, and G. Bauch, “Inactivation Decoding of LT and Raptor Codes: Analysis and Code Design”, IEEE Transactions on Communications 1 (2017) arXiv:1706.05814 DOI

## Page edit log

- Victor V. Albert (2022-05-25) — most recent
- Thomas Wrona (2022-04-11)

## Cite as:

“Raptor (RAPid TORnado) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/raptor

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/fountain/raptor.yml.