Approximating the capacity of wireless multiple unicast networks by discrete superposition model

The discrete superposition model (DSM) is intended to approximate the capacity region of AWGN networks. Finding the capacity region in the DSM is simpler due to its discrete and deterministic properties. For unicast in relay networks and for the multi-user interference channel it has been shown that the capacity regions of the DSM and of the AWGN model are within a constant gap. We extend this result to multiple unicast in networks consisting of broadcast and multiple-access channels by using a recent result on polymatroidal networks. We show that the capacity regions of the two models are within a constant additive gap and a constant multiplicative gap.