Coding for Errors and Erasures in Random Network Coding

The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear networ...

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Bibliographische Detailangaben
Veröffentlicht in:	IEEE transactions on information theory Jg. 54; H. 8; S. 3579 - 3591
Hauptverfasser:	Koetter, R., Kschischang, F.R.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York, NY IEEE 01.08.2008 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Applied sciences Codes Coding Coding, codes Construction Context modeling Cryptography Data encryption Decoding Detection, estimation, filtering, equalization, prediction Error correction Error correction codes Errors Exact sciences and technology Geometry Information theory Information, signal and communications theory Jamming Mathematical models Network coding network error correction Networks Receivers Signal and communications theory Signal, noise Strontium subspace metric Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Transmission and modulation (techniques and equipments) Transmitters Vector spaces Vectors Reed Solomon code Finite field Parameter estimation sub- space metric Coding errors Transfer characteristic Transmitter Decoding Geometrical projection Random coding Algorithm Information transmission network error correction Linear coding Vector space Channel estimation Network coding Minimal distance Metric Error correction
ISSN:	0018-9448, 1557-9654
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	The problem of error-control in random linear network coding is considered. A ldquononcoherentrdquo or ldquochannel obliviousrdquo model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that linear network coding is vector-space preserving, information transmission is modeled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U . A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum-distance decoder for this metric achieves correct decoding if the dimension of the space V cap U is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. Sphere-packing and sphere-covering bounds as well as a generalization of the singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is described and a Sudan-style ldquolist-1rdquo minimum-distance decoding algorithm is provided.
Bibliographie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2008.926449