Randomized algorithms
An algebraic approach to network coding
IEEE/ACM Transactions on Networking (TON)
Improving the multicommodity flow rates with network codes for two sources
IEEE Journal on Selected Areas in Communications - Special issue on network coding for wireless communication networks
Pairwise intersession network coding on directed networks
IEEE Transactions on Information Theory
Overlay protection against link failures using network coding
IEEE/ACM Transactions on Networking (TON)
Insufficiency of linear coding in network information flow
IEEE Transactions on Information Theory
On the capacity of information networks
IEEE Transactions on Information Theory
The encoding complexity of network coding
IEEE Transactions on Information Theory
A Random Linear Network Coding Approach to Multicast
IEEE Transactions on Information Theory
Interference Alignment and Degrees of Freedom of the -User Interference Channel
IEEE Transactions on Information Theory
Algebraic Algorithms for Vector Network Coding
IEEE Transactions on Information Theory
Network Coding Games with Unicast Flows
IEEE Journal on Selected Areas in Communications
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We consider the multiple-unicast problem with three source–terminal pairs over directed acyclic networks with unit-capacity edges. The three $s_i{\hbox{–}}t_i$ pairs wish to communicate at unit-rate via network coding. The connectivity between the $s_i{\hbox{–}}t_i$ pairs is quantified by means of a connectivity-level vector, $[k_1\ k_2\ k_3]$ such that there exist $k_i$ edge-disjoint paths between $s_i$ and $t_i$. In this paper, we attempt to classify networks based on the connectivity level. It can be observed that unit-rate transmission can be supported by routing if $k_i \geq 3$, for all $i = 1, \ldots, 3$. In this paper, we consider connectivity-level vectors such that $\min_{i = 1, \ldots, 3} k_i . We present either a constructive linear network coding scheme or an instance of a network that cannot support the desired unit-rate requirement, for all such connectivity-level vectors except the vector [1 2 4] (and its permutations). The benefits of our schemes extend to networks with higher and potentially different edge capacities. Specifically, our experimental results indicate that for networks where the different source–terminal paths have a significant overlap, our constructive unit-rate schemes can be packed along with routing to provide higher throughput as compared to a pure routing approach.