Open AccessProceedings Article
Raptor codes
Amin Shokrollahi
- 01 Jan 2004
1.5K
TL;DR: For a given integer k, and any real /spl epsiv/>0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1 + /spl Epsiv/) is sufficient to recover the original k symbols, with high probability as mentioned in this paper.
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Abstract: This paper exhibits a class of universal Raptor codes: for a given integer k, and any real /spl epsiv/>0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1 + /spl epsiv/) is sufficient to recover the original k symbols, with high probability. Each output symbol is generated using O(log(1//spl epsiv/)) operations, and the original symbols are recovered from the collected ones with O(klog(1//spl epsiv/)) operations.
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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
LT codes
Michael Luby
- 16 Nov 2002
TL;DR: LT codes are introduced, the first rateless erasure codes that are very efficient as the data length grows, and are based on EMMARM code, which was introduced in version 2.0.
3.2K
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.