In a wireless network with a single source and a single destination and an arbitrary number of relay nodes, what is the maximum rate of information flow achievable? We make progress on this long standing problem through a two-step approach. First, we propose a deterministic channel model which captures the key wireless propertiesofsignalstrength,broadcastandsuperposition. We obtain an exact characterization of the capacity of a network with nodes connected by such deterministic channels. This result is a natural generalization of the celebrated max-flow min-cut the- orem for wired networks. Second, we use the insights obtained from the deterministic analysis to design a new quantize-map-and- forward scheme for Gaussian networks. In this scheme, each relay quantizes the received signal at the noise level and maps it to a random Gaussian codeword for forwarding, and the final destina- tion decodes the source's message based on the received signal. We show that, in contrast to existing schemes, this scheme can achieve the cut-set upper bound to within a gap which is independent of the channel parameters. In the case of the relay channel with a single relay as well as the two-relay Gaussian diamond network, the gap is 1 bit/s/Hz. Moreover, the scheme is universal in the sense that the relays need no knowledge of the values of the channel pa- rameters to (approximately) achieve the rate supportable by the network. We also present extensions of the results to multicast net- works, half-duplex networks, and ergodic networks.

Journal: IEEE Transactions on Information Theory - TIT, vol. 57, no. 4, pp. 1872-1905, 2011

]]>