Coding for Errors and Erasures in Random Network Coding

Abstract

The problem of error-control in a "noncoherent" random network coding channel is considered. 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. A suitable coding metric on subspaces is defined, under which a minimum distance decoder achieves correct decoding if the dimension of the space V U is large enough. When the dimension of each codeword is restricted to a fixed integer, the code forms a subset of the vertices of the Grassmann graph. Sphere-packing, sphere-covering bounds and a Singleton bound are provided for such codes. A Reed-Solomon-like code construction is provided and decoding algorithm given.