Raptor codes

LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor code...

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Published in:IEEE transactions on information theory Vol. 52; no. 6; pp. 2551 - 2567
Main Author: Shokrollahi, A.
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2006
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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ISSN:0018-9448, 1063-6692, 1557-9654, 1558-2566
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Abstract LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integer k and any real epsiv>0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1+epsiv) is sufficient to recover the original k symbols with high probability. Each output symbol is generated using O(log(1/epsiv)) operations, and the original symbols are recovered from the collected ones with O(klog(1/epsiv)) operations. We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements
AbstractList LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integer k and any real epsiv>0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1+epsiv) is sufficient to recover the original k symbols with high probability. Each output symbol is generated using O(log(1/epsiv)) operations, and the original symbols are recovered from the collected ones with O(klog(1/epsiv)) operations. We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements
LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integerkand any real varepsilon ≫0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of sizek(1 varepsilon )is sufficient to recover the originalksymbols with high probability. Each output symbol is generated usingO(log (1/ varepsilon ))operations, and the original symbols are recovered from the collected ones withO(klog (1/ varepsilon ))operations. We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the originalkelements.
LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit 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. We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements. [PUBLICATION ABSTRACT]
LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integer k and any real epsilon > 0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k(1 + epsilon) is sufficient to recover the original k symbols with high probability. Each output symbol is generated using O(log(1/ epsilon)) operations, and the original symbols are recovered from the collected ones with O(k log(1/epsilon)) operations.We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements.
Special issue title: Special issue on networking and information theory LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integer k and any real ε > 0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k (1 + ε) is sufficient to recover the original k symbols with high probability. Each output symbol is generated using O (log(1/ ε)) operations, and the original symbols are recovered from the collected ones with O (k log(1/ε)) operations.We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements.
LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper, we introduce Raptor codes, an extension of LT-codes with linear time encoding and decoding. We will exhibit a class of universal Raptor codes: for a given integer k and any real E > 0, Raptor codes in this class produce a potentially infinite stream of symbols such that any subset of symbols of size k (1 + E) is sufficient to recover the original k symbols with high probability. Each output symbol is generated using O (log(1/ E)) operations, and the original symbols are recovered from the collected ones with O (k log(1/E)) operations.We will also introduce novel techniques for the analysis of the error probability of the decoder for finite length Raptor codes. Moreover, we will introduce and analyze systematic versions of Raptor codes, i.e., versions in which the first output elements of the coding system coincide with the original k elements. [PUBLICATION ABSTRACT]
Author Shokrollahi, A.
Author_xml – sequence: 1
  givenname: A.
  surname: Shokrollahi
  fullname: Shokrollahi, A.
  organization: Sch. of Comput. Sci. & Commun., Sch. of Basic Sci
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Cites_doi 10.1109/TIT.2002.1003839
10.1109/TIT.2005.850079
10.1109/18.910575
10.1145/285243.285258
10.7551/mitpress/4347.001.0001
10.1109/18.910576
10.1007/3-540-46796-3_7
10.1109/SFCS.2002.1181950
10.1109/ISIT.2004.1365074
10.1109/TIT.2002.805067
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References ref13
Shokrollahi (ref17) 2001
Luby (ref5) 2001
ref15
ref14
Jin (ref12)
ref20
Shokrollahi (ref22) 2005
ref11
Maymounkov (ref9) 2002
(ref10) 2005
Luby (ref18)
ref2
Luby (ref6) 2002
ref16
Shokrollahi (ref8) 2001
ref7
ref4
ref3
Luby (ref19) 2001
Shokrollahi (ref21) 2005
Elias (ref1)
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  doi: 10.1109/TIT.2002.1003839
– ident: ref13
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– volume-title: Finite Length Analysis of a Certain Class of LDPC Codes
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– ident: ref2
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– volume-title: Information Additive Code Generator and Decoder for Communication Systems
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– ident: ref4
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– ident: ref14
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– ident: ref15
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– volume-title: 3rd Generation Partnership Project (3GPP)
  year: 2005
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– ident: ref7
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– ident: ref16
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  year: 2001
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Snippet LT-codes are a new class of codes introduced by Luby for the purpose of scalable and fault-tolerant distribution of data over computer networks. In this paper,...
Special issue title: Special issue on networking and information theory LT-codes are a new class of codes introduced by Luby for the purpose of scalable and...
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SubjectTerms Binary erasure channel (BEC)
Buffer overflow
Codes
Coding
Computer networks
Decoders
Decoding
Error analysis
Error probability
Fault tolerance
graphical codes
Internet
Large-scale systems
LT-codes
Mathematical analysis
networking
Probability
Protocols
Scalability
Streams
Studies
Symbols
Title Raptor codes
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