A Subspace Approach to Error Control in Random Network Coding Professor Frank R. Kschischang Dept. of Electrical and Computer Engineering University of Toronto Thursday, Oct 25, 11am SITE 5084, 800 King Edward Ave Sponsored  by Bell Advanced Research Laboratory

Random network coding is a powerful tool for efficient information dissemination in networks, wherein information is transmitted as fixed-length vectors over a finite field F, and intermediate nodes are permitted to forward random F-linear combinations of packets that they receive. Unfortunately, random network coding is highly susceptible to errors caused by noise, intentional jamming, or packet losses.

In this talk I will describe a new approach to the problem of error-control in random network coding. Motivated by the property that, in the absence of errors, 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 over F and the collection by the receiver of a basis for a vector space U. After introducing a suitable metric on the collection of subspaces, I will show that a minimum distance decoder for this metric achieves correct decoding if the dimension of the intersection of V and U is large enough. If the dimension of each codeword is restricted to a fixed integer, the code corresponds to a well-separated subset of the vertices of a Grassmann graph. Sphere-packing and sphere-covering bounds as well as generalization of the Singleton bound are provided for such codes. Finally, I will describe a Reed-Solomon-like code construction and a decoding algorithm for error-and-erasure correction.

This is joint work with Ralf Koetter, Technical University of Munich.