Feedback via message passing in interference channels

In distributed wireless networks, nodes often do not know the topology (network size, connectivity and the channel gains) of the network. Thus, they have to compute their transmission and reception parameters in a distributed fashion. In this paper, we consider the information required at the nodes to achieve globally optimal sum capacity. Our first result relates to the case when each of the transmitter know the channel gains of all the links that are at-most two-hop distant from it and the receiver knows the channel gains of all the links that are three-hop distant from it in a deterministic interference channel. With this limited information, we find that distributed decisions are sum-rate optimal only if each connected component is in a one-to-many configuration or a fully-connected configuration. In all other cases of network connectivity, the loss can be arbitrarily large. We then extend the result to see that O(K) hops of information are needed in general to achieve globally optimal solutions. To show this we consider a class of symmetric interference channel chain and find that in certain cases of channel gains, the knowledge of a particular user being odd user or even user is important thus needing O(K) hops of information at the nodes.