Coding for the deterministic network model

The capacity of multiuser networks has been a long-standing problem in information theory. Recently, Avestimehr et al. have proposed a deterministic network model to approximate wireless networks. For multicast, they have shown that the capacity for the deterministic model is equal to the minimal rank of the incidence matrix of a certain cut between the source and any of the sinks. Their proposed code construction, however, is not guaranteed to be efficient and may potentially involve an infinite block length. We propose an efficient linear code construction for the deterministic wireless multicast relay network model. Unlike several previous coding schemes, we do not attempt to find flows in the network. Instead, we maintain an invariant where it is required that at each stage of the code construction, certain sets of codewords are linearly independent.