Journal Article10.1561/0100000060
Raptor Codes
Amin Shokrollahi,Michael Luby +1 more
330
TL;DR: In this paper, the theory behind Raptor codes and the processes behind the design of two of the most prominent members of this class of codes: R10 and RaptorQ (RQ).
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Abstract: This monograph describes the theory behind Raptor codes, and elucidates elements of the processes behind the design of two of the most prominent members of this class of codes: R10 and RaptorQ (RQ). R10 has already been adopted by a number of standards' bodies, and RQ is in the process of entering various standards at the time of writing of this monograph.
The monograph starts with the description of some of the transmission problems, which inspired the invention of Fountain codes. Thereafter, Luby transform codes (LT codes) and Raptor codes are introduced and insights are provided into their design. These codes are currently the most efficient realizations of Fountain codes. Different algorithms are introduced for encoding and decoding various versions of these codes, including their systematic versions. Moreover, a hybrid decoding algorithm called "inactivation decoding" is introduced, which is an integral part of all modern implementations of Raptor codes.
The R10 and RQ codes have been continued and will continue to be adopted into a number of standards and thus there are publicly available specifications that describe exactly how to implement these codes. However, the standards' specifications provide no insight into the rationale for the design choices made. One of the primary purposes of this document is to provide this design rationale.
We provide results of extensive simulations of R10 and RQ codes to show the behavior of these codes in many different scenarios.
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References
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Low-Density Parity-Check Codes
Robert G. Gallager
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TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
•Proceedings Article
Raptor Codes
Amin Shokrollahi
- 01 Jul 2007
TL;DR: In this paper, the authors introduce several classes of probabilistic Fountain codes, including LT-and Raptor codes, and discuss how they are used today to solve various data transmission problems on heterogeneous unreliable networks.
2.2K
Efficient erasure correcting codes
TL;DR: A simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs is introduced and a simple criterion involving the fractions of nodes of different degrees on both sides of the graph is obtained which is necessary and sufficient for the decoding process to finish successfully with high probability.
A digital fountain approach to reliable distribution of bulk data
John W. Byers,Michael Luby,Michael Mitzenmacher,Ashutosh Rege +3 more
- 01 Oct 1998
TL;DR: A protocol is developed that closely approximates a digital fountain using a new class of erasure codes that for large block sizes are orders of magnitude faster than standard erasures codes.
Efficient encoding of low-density parity-check codes
TL;DR: It is shown how to exploit the sparseness of the parity-check matrix to obtain efficient encoders and it is shown that "optimized" codes actually admit linear time encoding.