Approximate Characterization of Capacity in Gaussian Relay Networks

One of the distinguishing features of wireless communication is its broadcast nature. This creates complicated signal interactions when there are multiple transmitting and receiving nodes, due to superposition of signals at the receivers. In this paper, we focus on wireless relay networks where (relay) nodes facilitate communications between a source and a destination. We review some recent progress on this problem. The progress is made by developing simpler models which give insight and facilitate an approximate characterization of network capacity. We have developed deterministic models that (approximately) capture these interactions and show that for such models, one can obtain an information-theoretic max-flow min-cut result, in analogy to the classic wire-line Ford-Fulkerson result. We have extended these ideas to networks with general deterministic (interaction) functions. Using insights from the analysis of deterministic networks, we develop an approximate characterization for noisy Gaussian relay networks showing that the achievable rate is within a constant number of bits from the information- theoretic cut-set upper bound on the capacity of these networks. This constant depends on the topology of the network, but not on the values of the channel gains.