Achieving the capacity of the N-relay Gaussian diamond network within logn bits

We consider the N-relay Gaussian diamond network where a source node communicates to a destination node via N parallel relays. We show that several strategies can achieve the capacity of this network within O(log N) bits independent of the channel configurations and the operating SNR. The first of these strategies is partial decode-and-forward: the source node broadcasts independent messages to the relays at appropriately chosen rates, which in turn decode and forward these messages to the destination over a MAC channel. The same performance can be also achieved by compress-and-forward, quantize-map-and-forward or noisy network coding if relays quantize their observations at a decreasing resolution with N, instead of quantizing at the noise-level. The best capacity approximations currently available for this network are within O(N) bits which follow from the corresponding capacity approximations for general Gaussian relay networks.