A Rank-Metric Approach to Error Control in Random Network Coding
By Danilo Silva, Frank R. Kschischang, Ralf Koetter. IEEE Transactions on Information Theory, 2007
580 citations recorded by the source corpus.
The problem of error control in random linear network coding is addressed from a matrix perspective that is closely related to the subspace perspective of Rotter and Kschischang. A large class of constant-dimension subspace codes is investigated. It is shown that codes in this class can be easily constructed from rank-metric codes, while preserving their distance properties. Moreover, it is shown that minimum distance decoding of such subspace codes can be reformulated as a generalized decoding problem for rank-metric codes where partial information about the error is available. This partial information may be in the form of erasures (knowledge of an error location but not its value) and deviations (knowledge of an error value but not its location). Taking erasures and deviations into account (when they occur) strictly increases the error correction capability of a code: if mu erasures and delta deviations occur, then errors of rank t can always be corrected provided that 2t les d - 1 + mu + delta, where d is the minimum rank distance of the code. For Gabidulin codes, an important family of maximum rank distance codes, an efficient decoding algorithm is proposed that can properly exploit erasures and deviations. In a network coding application, where n packets of length M over F(q) are transmitted, the complexity of the decoding algorithm is given by O(dM) operations in an extension field F(qn).
Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering
View Paper: https://www.semanticscholar.org/paper/fe09aba19eb8661c20c3c9e21d2b78c996995e68
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
In Computer Networks and Communications
In Electrical and Electronic Engineering
Citations in the corpus
- New semifields and new MRD codes from skew polynomial rings (2018, background): “Rank-metric codes have been studied in recent years in part due to their potential applications in random network coding; see for example [46].”
- MRD Codes: Constructions and Connections (2019, methodology): “Subspace codes have applications in random network coding, due to the influential work of Koetter-Kchishang [54], [97].”