  New achievable rate regions are derived for the two-user additive white
Gaussian multiple-access channel with noisy feedback. The regions exhibit the
following two properties. Irrespective of the (finite) Gaussian feedback-noise
variances, the regions include rate points that lie outside the no-feedback
capacity region, and when the feedback-noise variances tend to 0 the regions
converge to the perfect-feedback capacity region. The new achievable regions
also apply to the partial-feedback setting where one of the transmitters has a
noisy feedback link and the other transmitter has no feedback at all. Again,
irrespective of the (finite) noise variance on the feedback link, the regions
include rate points that lie outside the no-feedback capacity region. Moreover,
in the case of perfect partial feedback, i.e., where the only feedback link is
noise-free, for certain channel parameters the new regions include rate points
that lie outside the Cover-Leung region. This answers in the negative the
question posed by van der Meulen as to whether the Cover-Leung region equals
the capacity region of the Gaussian multiple-access channel with perfect
partial feedback. Finally, we propose new achievable regions also for a setting
where the receiver is cognizant of the realizations of the noise sequences on
the feedback links.
