Despite the famous ''everybody eats half of the cake'' promise, schemes achieving 1/2 DoFs per user in general fully connected Gaussian networks require precoding over a signal space of asymptotically large diversity, e.g., over an infinite number of dimensions for time-frequency varying fading channels, or over an infinite number of rationally independent signal levels. In this talk we consider a recently proposed scenario inspired to the regular lattice-like topology of cellular systems where the promised optimal DoFs are achieved with linear ''one-shot'' precoding (i.e., over a single time-frequency slot). We consider the uplink of a symmetric cellular system, and consider both sectorization and isotropic cells, where interfrerence comes form the neighboring sectors (in the first case) or from the neighboring cells (in the second case). At the base station receiver side, we consider a message-passing scheme where nearby base stations can exchange already decoded messages. Notice that this network architecture is much simpler and involve much less backhaul rate requirements than the classical ''Wyner model'' type of networks, with fully centralized receiver processing. Our alignment & (local) interference cancellation solution achieves the optimal DoFs for the second configurations with M antennas at each transmitter and receiver, and in the isotropic cell scenario with M = 2 antennas. For the latter case, we also present non-trivial achievable DoFs schemes in the case where the mobiles have 2 antennas and the base stations have 3 and 4 antennas. Furthermore, in order to avoid signaling scheme relying on the strength of interference, we further introduce the notion of topologically robust schemes, which are able to guarantee a minimum rate (or DoFs) irrespectively of the strength of the interfering links. Towards this end, for the MxM sector case, we propose an alignment scheme which is topologically robust and still achieves the same optimum DoFs. Finally, we present a novel DoFs uplink-downlink duality result which proves that whatever DoFs can be achieved in the uplink the decoded message sharing and alignment scheme, they can be also achieved in the downlink through a ''dual'' precoding scheme that involves only cooperation among neighboring base stations, which are required to share ''quantized'' versions of their dirty-paper coded signals. In contrast to virtually any known result on downlink DoFs, this scheme required dirty-paper coding which cannot be replaced with the more familiar linear zero-forcing precoding.
This is joint work with Vasilis Ntranos (USC), and Mohammad Maddah-Ali (Bell Labs).