On the asymptotic capacity of Gaussian relay networks

In this paper, we determine the asymptotic capacity of a Gaussian multiple-relay channel as the number of relays tends to infinity. The upper bound is an application of the cut-set theorem, and the lower bound follows from an argument involving uncoded transmission. Hence, this paper gives one more example where the cut-set bound is achievable, and one more example where uncoded transmission achieves optimal performance. In the latter sense, the result is an extension to [1]. The arguments of this paper are also relevant to wireless networks, yielding an asymptotic capacity result [2].