An improved upper bound on network function computation using cut-set partition

Abstract

The network function computation in directed acyclic networks is investigated in this paper. In such a network, a sink node desires to correctly compute a target function, of which all inputs are generated at multiple source nodes. The network links are assumed to be error-free and have limited capacity. The intermediate nodes can perform network coding. The computing rate of a network code is measured by the average number of times that the target function can be computed for one use of the network. In the paper, by using a cut-set partition approach to refine the equivalence classes associated with the inputs of the target function, a general upper bound on the network computing capacity is obtained, which is applicable to arbitrary target functions and network topologies. It is shown that this new upper bound is in general strictly better than the best existing one proposed by Huang, Tan and Yang.