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.

Biography of Frank R. Kschischang

Frank R. Kschischang is a Professor in the Department of Electrical and Computer Engineering at the University of Toronto, where he holds the Tier-I Canada Research Chair in Communications Algorithms. He received the B.A.Sc. degree from the University of British Columbia in 1985 and M.A.Sc. and Ph.D. degrees from the University of Toronto in 1988 and 1991, respectively, all in electrical engineering. A former associate editor for Coding Theory of the IEEE Transactions on Information Theory, he is now a member of the Board of Governors of the IEEE Information Theory society. He served as technical program co-chair for the 2004 IEEE International Symposium on Information Theory (ISIT) held in Chicago, and serves as general co-chair for the 2008 ISIT, which will be held in Toronto. A popular teacher, Professor Kschischang has three times been voted "Professor of the Year" by undergraduate students, and he received the University of Toronto Faculty of Applied Science and Engineering Faculty Teaching Award in 2006. He is a recipient of the Ontario Premier's Research Excellence Award. He is a Fellow of the Engineering Institute of Canada and also a Fellow of IEEE.


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