Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Linear Network Error Correction Codes in Packet Networks
IEEE Transactions on Information Theory
Resilient Network Coding in the Presence of Byzantine Adversaries
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
A Rank-Metric Approach to Error Control in Random Network Coding
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
Packing and covering properties of subspace codes for error control in random linear network coding
IEEE Transactions on Information Theory
Constant-rank codes and their connection to constant-dimension codes
IEEE Transactions on Information Theory
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Communication over finite-field matrix channels
IEEE Transactions on Information Theory
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The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and destination nodes, the error correction capability of an (outer) code is succinctly described by the rank metric; as a consequence, it is shown that universal network error correcting codes achieving the Singleton bound can be easily constructed and efficiently decoded. For noncoherent network coding, where knowledge of the network topology and network code is not assumed, the error correction capability of a (subspace) code is given exactly by a new metric, called the injection metric, which is closely related to, but different than, the subspace metric of Kötter and Kschischang. In particular, in the case of a non-constant-dimension code, the decoder associated with the injection metric is shown to correct more errors then a minimum-subspace-distance decoder. All of these results are based on a general approach to adversarial error correction, which could be useful for other adversarial channels beyond network coding.