Coding for Errors and Erasures in Random Network Coding

Abstract—The problem of error-control in random linear network coding is considered. A “noncoherent” or “channel oblivious” 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 vectorspace 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 \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 ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Ralf Koetter, Frank R. Kschischang
• Keywords: CORR 2007, Education, Random Linear Network, Vector Space, Vector Space U