On the asymptotic capacity of Gaussian relay networks
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 of the work of Gastpar, Rimoldi and Vetterli (see IEEE Trans. Info. Theory, May 2001). The arguments of this paper are also relevant to wireless networks, yielding an asymptotic capacity result.