Abstract
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.
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| 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.
This website is maintained by Yongyi Mao, and was last
updated on Sep. 24, 2007
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