On the capacity of multisource non-coherent network coding

We consider multisource non-coherent network coding, where multiple sources send information to one or multiple receivers. We prove that this is equivalent to a “subspace” channel, that takes subspaces as inputs and outputs. We then show that the rate of each individual receiver is upper bounded as δ i (T−δ 1 −δ 2 ), where δ i is what we define to be the “dominating” dimension in the subspace codebook of source i, and T is the “coherence” time of the network.