Decoding of random network codes

We consider the decoding for Silva-Kschischang-Kötter random network codes based on Gabidulin’s rank-metric codes. The model of a random network coding channel can be reduced to transmitting matrices of a rank code through a channel introducing three types of additive errors. The first type is called random rank errors. To describe other types, the notions of generalized row erasures and generalized column erasures are introduced. An algorithm for simultaneous correction of rank errors and generalized erasures is presented. An example is given.

[1]  Ernst M. Gabidulin.  A Fast Matrix Decoding Algorithm for Rank-Error-Correcting Codes , 1991, Algebraic Coding.

[2]  Martin Bossert,et al.  Space-time codes based on rank codes , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[3]  Frank R. Kschischang,et al.  Coding for Errors and Erasures in Random Network Coding , 2007, IEEE Transactions on Information Theory.

[4]  Frank R. Kschischang,et al.  A Rank-Metric Approach to Error Control in Random Network Coding , 2007, IEEE Transactions on Information Theory.

[5]  Frank R. Kschischang,et al.  Fast encoding and decoding of Gabidulin codes , 2009, 2009 IEEE International Symposium on Information Theory.

[6]  Philippe Delsarte,et al.  Bilinear Forms over a Finite Field, with Applications to Coding Theory , 1978, J. Comb. Theory A.

[7]  Martin Bossert,et al.  Correcting generalized matrix erasures with applications to random network coding , 2010, 2010 International ITG Conference on Source and Channel Coding (SCC).

[8]  Pierre Loidreau,et al.  A Welch-Berlekamp Like Algorithm for Decoding Gabidulin Codes , 2005, WCC.

[9]  Simon Plass,et al.  Fast decoding of rank-codes with rank errors and column erasures , 2004, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[10]  Ernst M. Gabidulin,et al.  Error and erasure correcting algorithms for rank codes , 2008, Des. Codes Cryptogr..