Robust Network Function Computation

We consider the following robust computing problem in a directed acyclic network. A sink node is required to compute with zero error a target function of source messages which are generated at multiple source nodes, whereas the communication links might be corrupted by errors. The nodes in this network may perform network coding to combat the errors. Given an integer τ, the robust computing rate of a network code against τ errors is the average number of times that the target function can be computed with zero error for one use of the network with at most τ links being corrupted by errors. We derive two cut-set bounds on the robust computing capacity and show that these bounds can be achieved in a multi-edge tree network for computing any target function. Furthermore, we consider linear network codes for computing linear target functions. Given a computing rate, we define a minimum distance to measure the error-tolerant capability of the linear network function computing codes. We propose a Singleton-like bound on this minimum distance and show that this bound is tight in two classes of networks for computing the sum of source messages.