The rank of sparse random matrices over finite fields
Random Structures & Algorithms
Handbook of Coding Theory
On the capacity of non-coherent network coding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
IEEE Transactions on Information Theory
Coding for Errors and Erasures in Random Network Coding
IEEE Transactions on Information Theory
Improved compression of network coding vectors using erasure decoding and list decoding
IEEE Communications Letters
Compressed error and erasure correcting codes via rank-metric codes in random network coding
International Journal of Communication Systems
SenseCode: Network coding for reliable sensor networks
ACM Transactions on Sensor Networks (TOSN)
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In networks that employ network coding, two main approaches have been proposed in the literature to allow the receivers to recover the source information: (i) use of coding vectors, that keep track of the linear combinations the received packets contain, and (ii) subspace coding, that dispenses of the need to know the linear combinations, since information is conveyed from the choice of subspaces alone. Both these approaches impose the strong requirement that all source packets get potentially combined. We here present a third approach that relaxes this assumption, and is thus not a special case from either of the previous two. This relaxation allows to employ compressed coding vectors to efficiently convey the coding coefficients, without altering the operation of intermediate network nodes. We develop optimal designs for such vectors.