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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| Vydáno v: | IEEE transactions on information theory Ročník 52; číslo 6; s. 2551 - 2567 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
IEEE
01.06.2006
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Témata: | |
| ISSN: | 0018-9448, 1063-6692, 1557-9654, 1558-2566 |
| On-line přístup: | Získat plný text |
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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 |
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| AbstractList | 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] 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. |
| 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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| CODEN | IETTAW |
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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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| 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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