  The adaptive zero-error capacity of discrete memoryless channels (DMC) with
noiseless feedback has been shown to be positive whenever there exists at least
one channel output "disprover", i.e. a channel output that cannot be reached
from at least one of the inputs. Furthermore, whenever there exists a
disprover, the adaptive zero-error capacity attains the Shannon (small-error)
capacity. Here, we study the zero-error capacity of a DMC when the channel
feedback is noisy rather than perfect. We show that the adaptive zero-error
capacity with noisy feedback is lower bounded by the forward channel's
zero-undetected error capacity, and show that under certain conditions this is
tight.
