  In this paper, we study the capacity regions of two-way diamond channels. We
show that for a linear deterministic model the capacity of the diamond channel
in each direction can be simultaneously achieved for all values of channel
parameters, where the forward and backward channel parameters are not
necessarily the same. We divide the achievability scheme into three cases,
depending on the forward and backward channel parameters. For the first case,
we use a reverse amplify-and-forward strategy in the relays. For the second
case, we use four relay strategies based on the reverse amplify-and-forward
with some modifications in terms of replacement and repetition of some stream
levels. For the third case, we use two relay strategies based on performing two
rounds of repetitions in a relay. The proposed schemes for deterministic
channels are used to find the capacity regions within constant gaps for two
special cases of the Gaussian two-way diamond channel. First, for the general
Gaussian two-way relay channel with a simple coding scheme the smallest gap is
achieved compared to the prior works. Then, a special symmetric Gaussian
two-way diamond model is considered and the capacity region is achieved within
four bits.
