On the variable-delay reliability function of discrete memoryless channels with access to noisy feedback

We give a scheme for variable-delay reliable communication over a noisy discrete memoryless channel with a noisy feedback DMC being available between the receiver and the transmitter. This scheme works when the capacity of the feedback channel is greater than the capacity of the forward channel and the target rate of communication on the forward channel is less than its capacity. Rather than looking at a single block in isolation, we consider the scenario where we expect this system to carry an infinite stream of packets. We show that in the limit of nearly noiseless feedback channels, we approach the Burnashev bound on the reliability of variable-delay channel codes.