  In a recent paper [4], Mari\'c et al. analyzed the performance of the analog
network coding (ANC) in a layered relay network for the high-SNR regime. They
have proved that under the ANC scheme, if each relay transmits the received
signals at the upper bound of the power constraint, the transmission rate will
approach the network capacity. In this paper, we consider a more general
scenario defined as the generalized high-SNR regime, where the relays at layer
$l$ in a layered relay network with $L$ layers do not satisfy the high-SNR
conditions, and then determine an ANC relay scheme in such network. By relating
the received SNR at the nodes with the propagated noise, we derive the rate
achievable by the ANC scheme proposed in this paper. The result shows that the
achievable ANC rate approaches the upper bound of the ANC capacity as the
received powers at relays in high SNR increase. A comparison of the two ANC
schemes implies that the scheme proposed in [4] may not always be the optimal
one in the generalized high-SNR regime. The result also demonstrates that the
upper and lower bounds of the ANC rate coincide in the limit as the number of
relays at layer L-1 dissatisfying the high-SNR conditions tends to infinity,
yielding an asymptotic capacity result.
