Deterministic network coding algorithms and applications for wireless networks

We give new deterministic and randomized algorithms for the wireless model of Avestimehr, Diggavi, Tse for Gaussian relay networks by reducing it to the more general deterministic network coding problem introduced by Harvey, Karger and Murota. We also give a sufficient condition for a subset of coding coefficients which can be fixed arbitrarily to nonzero values, and the remaining coefficients can be determined in order to have a feasible network code. Finally we present applications to networks with nodes of different transmission properties.