  The Gaussian parallel relay network, in which two parallel relays assist a
source to convey information to a destination, was introduced by Schein and
Gallager. An upper bound on the capacity can be obtained by considering
broadcast cut between the source and relays and multiple access cut between
relays and the destination. Niesen and Diggavi derived an upper bound for
Gaussian parallel $N$-relay network by considering all other possible cuts and
showed an achievability scheme that can attain rates close to the upper bound
in different channel gain regimes thus establishing approximate capacity. In
this paper we consider symmetric layered Gaussian relay networks in which there
can be many layers of parallel relays. The channel gains for the channels
between two adjacent layers are symmetrical (identical). Relays in each layer
broadcast information to the relays in the next layer. For 2-layer $N$-relay
Gaussian network we give upper bounds on the capacity. Our analysis reveals
that for the upper bounds, joint optimization over correlation coefficients is
not necessary for obtaining stronger results.
