Overview
Raptor codes are formed by the concatenation of two codes.
A fixed rate erasure code, usually with a fairly high rate, is applied as a 'pre-code' or 'outer code'. This pre-code may itself be a concatenation of multiple codes, for example in the code standardized by 3GPP a high density parity check code derived from the binary Gray sequence is concatenated with a simple regular low density parity check code. Another possibility would be a concatenation of a Hamming code with a low density parity check code.
The inner code takes the result of the pre-coding operation and generates a sequence of encoding symbols. The inner code is a form of LT codes. Each encoding symbol is the XOR of a randomly chosen set of symbols from the pre-code output. The number of symbols which are XOR'ed together to form an output symbol is chosen randomly for each output symbol according to a specific probability distribution.
This distribution, as well as the mechanism for generating random numbers for sampling this distribution and for choosing the symbols to be XOR'ed, must be known to both sender and receiver. In one approach, each symbol is accompanied with an identifier which can be used as a seed to a pseudo-random number generator to generate this information, with the same process being followed by both sender and receiver.
In the case of non-systematic raptor codes, the source data to be encoded is used as the input to the pre-coding stage.
In the case of systematic raptor codes, the input to the pre-coding stage is obtained by first applying the inverse of the encoding operation that generates the first k output symbols to the source data. Thus, applying the normal encoding operation to the resulting symbols causes the original source symbols to be regenerated as the first k output symbols of the code. It is necessary to ensure that the random processes which generate the first k output symbols generate an operation which is invertible.
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