Computer Science – Information Theory
Scientific paper
2007-03-13
Computer Science
Information Theory
This revised paper contains some minor changes and clarifications
Scientific paper
The problem of error-control in random linear 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 linear 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 $U$. A metric on the projective geometry associated with the packet space is introduced, and it is shown that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space $V \cap U$ is sufficiently large. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finite-field Grassmannian, or, equivalently, a subset of the vertices of the corresponding Grassmann graph. 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 described and a Sudan-style ``list-1'' minimum distance decoding algorithm is provided.
Koetter Ralf
Kschischang Frank
No associations
LandOfFree
Coding for Errors and Erasures in Random Network Coding does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Coding for Errors and Erasures in Random Network Coding, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coding for Errors and Erasures in Random Network Coding will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-438778