Coding for Errors and Erasures in Random Network Coding
Abstract
The problem of error-control in random 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 random network coding is vector-space preserving, information transmission is modelled 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 $U$. We introduce a metric on the space of all subspaces of a fixed vector space, and show that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space $V \cap U$ is large enough. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian. Sphere-packing and sphere-covering bounds as well as a generalization of the Singleton bound are provided for such codes. Finally, a Reed-Solomon-like code construction, related to Gabidulin's construction of maximum rank-distance codes, is provided.
Keywords
All Related Versions
This publication has 0 references indexed in Scilit: