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The Gaussian parallel relay network, in which two parallel relays assist asource to convey information to a destination, was introduced by Schein andGallager. An upper bound on the capacity can be obtained by consideringbroadcast cut between the source and relays and multiple access cut betweenrelays and the destination. Niesen and Diggavi derived an upper bound forGaussian parallel $N$-relay network by considering all other possible cuts andshowed an achievability scheme that can attain rates close to the upper boundin different channel gain regimes thus establishing approximate capacity. Inthis paper we consider symmetric layered Gaussian relay networks in which therecan be many layers of parallel relays. The channel gains for the channelsbetween two adjacent layers are symmetrical (identical). Relays in each layerbroadcast information to the relays in the next layer. For 2-layer $N$-relayGaussian network we give upper bounds on the capacity. Our analysis revealsthat for the upper bounds, joint optimization over correlation coefficients isnot necessary for obtaining stronger results.

Upper Bounds on the Capacity of 2-Layer $N$-Relay Symmetric Gaussian Network