An overview of network coding for dynamically changing networks
International Journal of Autonomous and Adaptive Communications Systems
Code construction for multiple sources network coding
Proceedings of the 2009 MobiHoc S3 workshop on MobiHoc S3
Bounds on covering codes with the rank metric
IEEE Communications Letters
Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams
IEEE Transactions on Information Theory
On randomized linear network codes and their error correction capabilities
IEEE Transactions on Information Theory
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Construction and covering properties of constant-dimension codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Decoder error probability of bounded distance decoders for constant-dimension codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Rank q-cyclic and pseudo-q-cyclic codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Fast encoding and decoding of Gabidulin codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Packing and covering properties of subspace codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Design of efficient robust network codes for multicast connections
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
On noncoherent correction of network errors and erasures with random locations
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Multishot codes for network coding: bounds and a multilevel construction
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On metrics for error correction in network coding
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Convolutional codes for network-error correction
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Packing and covering properties of subspace codes for error control in random linear network coding
IEEE Transactions on Information Theory
Network coding tomography for network failures
INFOCOM'10 Proceedings of the 29th conference on Information communications
Constant-rank codes and their connection to constant-dimension codes
IEEE Transactions on Information Theory
Robust network coding in the presence of untrusted nodes
IEEE Transactions on Information Theory
Communication over finite-field matrix channels
IEEE Transactions on Information Theory
Recursive code construction for random networks
IEEE Transactions on Information Theory
Decoding of random network codes
Problems of Information Transmission
On (Partial) unit memory codes based on Gabidulin codes
Problems of Information Transmission
Robust network codes for unicast connections: a case study
IEEE/ACM Transactions on Networking (TON)
List decoding subspace codes from insertions and deletions
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Joint network/channel decoding for heterogeneous multi-source/multi-relay cooperative networks
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
An authentication code against pollution attacks in network coding
IEEE/ACM Transactions on Networking (TON)
Compressed error and erasure correcting codes via rank-metric codes in random network coding
International Journal of Communication Systems
Fast decoding of Gabidulin codes
Designs, Codes and Cryptography
Secret Error Control Codes Against Malicious Attacks in Random Multisource Network Coding
Wireless Personal Communications: An International Journal
Rank subcodes in multicomponent network coding
Problems of Information Transmission
On the practicality of cryptographic defences against pollution attacks in wireless network coding
ACM Computing Surveys (CSUR)
List decoding reed-solomon, algebraic-geometric, and gabidulin subcodes up to the singleton bound
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Information security in a random network coding network
Problems of Information Transmission
Asymptotic behaviour of codes in rank metric over finite fields
Designs, Codes and Cryptography
Hi-index | 755.38 |
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).