Function computation in networks: Duality and constant gap results

In the linear function computation problem, multiple source nodes communicate across a relay network to a single destination whose goal is to recover a linear function of the original source data. For the case when the relay network is a deterministic network, a duality relation is established between the linear function computation problem and the standard, well-known multicast problem. Using this relation, a compact sufficient condition is found describing those cases where the cut-set bound is tight. Then, these insight are used to develop results for the case where the relay network contains Gaussian superposition channels. Assuming the original source sequences are independent Gaussians, the resulting distortion for the recovery of their sum is found to within a constant gap.