  We obtain new outer bounds on the capacity regions of the two-user multiple
access channel with generalized feedback (MAC-GF) and the two-user interference
channel with generalized feedback (IC-GF). These outer bounds are based on the
idea of dependence balance which was proposed by Hekstra and Willems [1]. To
illustrate the usefulness of our outer bounds, we investigate three different
channel models. We first consider a Gaussian MAC with noisy feedback (MAC-NF),
where transmitter $k$, $k=1,2$, receives a feedback $Y_{F_{k}}$, which is the
channel output $Y$ corrupted with additive white Gaussian noise $Z_{k}$. As the
feedback noise variances become large, one would expect the feedback to become
useless, which is not reflected by the cut-set bound. We demonstrate that our
outer bound improves upon the cut-set bound for all non-zero values of the
feedback noise variances. Moreover, in the limit as $\sigma_{Z_{k}}^{2}\to
\infty$, $k=1,2$, our outer bound collapses to the capacity region of the
Gaussian MAC without feedback. Secondly, we investigate a Gaussian MAC with
user-cooperation (MAC-UC), where each transmitter receives an additive white
Gaussian noise corrupted version of the channel input of the other transmitter
[2]. For this channel model, the cut-set bound is sensitive to the cooperation
noises, but not sensitive enough. For all non-zero values of cooperation noise
variances, our outer bound strictly improves upon the cut-set outer bound.
Thirdly, we investigate a Gaussian IC with user-cooperation (IC-UC). For this
channel model, the cut-set bound is again sensitive to cooperation noise
variances but not sensitive enough. We demonstrate that our outer bound
strictly improves upon the cut-set bound for all non-zero values of cooperation
noise variances.
