Lattice Coding Increases Multicast Rates for Gaussian Multiple-Access Networks

We study the multicasting problem for additive white Gaussian noise (AWGN) networks with both point-to-point and multiple-access links. The recent discovery of network coding has shown that routing is suboptimal for networks of point-topoint channels: messages must be mixed at intermediate nodes. We showed in earlier work that if a network includes multipleaccess channels (MACs) then converting these channels into bit pipes with a channel-network separation-based approach is also suboptimal: the MACs should be used to compute functions reliably as part of an overall network code. In this paper, we give a lattice-based coding strategy for reliably computing linear functions over Gaussian MACs. We then give a computable statement of rates achieved by the resulting network code. In many interesting cases, our achieved rates are higher than those accessible to a separation-based scheme. Our results show that structured codes can be used to derive achievable rates for multiuser communication problems that have been outside the reach of standard i.i.d. random coding arguments.