Foundations and Trends® in Networking
General Scheme for Perfect Quantum Network Coding with Free Classical Communication
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Feasible alphabets for communicating the sum of sources over a network
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
A constant bound on throughput improvement of multicast network coding in undirected networks
IEEE Transactions on Information Theory
On the multiple unicast network coding conjecture
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
| Hi-index | 754.90 |
We prove that for any finite directed acyclic network, there exists a corresponding multiple-unicast network, such that for every alphabet, each network is solvable if and only if the other is solvable, and, for every finite-field alphabet, each network is linearly solvable if and only if the other is linearly solvable. The proof is constructive and creates an extension of the original network by adding exactly s+5m(r-1) new nodes where, in the original network, m is the number of messages, r is the average number of receiver nodes demanding each source message, and s is the number of messages emitted by more than one source. The construction is then used to create a solvable multiple-unicast network which becomes unsolvable over every alphabet size if all of its edge directions are reversed and if the roles of source-receiver pairs are reversed