Inter-Modal Coding in Broadcast Packet Erasure Channels with Varying Statistics

We study the capacity region of the canonical two-user broadcast packet erasure channel when the erasure probabilities vary over the course of the communication block. In particular, we assume the network statistics may be in two distinct modes with a a priori known transition time between the two. We further consider the scenario in which the transmitter is informed of the delivery status of the previously transmitted packets through the feedback channel. We first derive a new set of the outer-bounds for this problem where the slope of the boundaries of the outer-bound region is dominated by the mode with the larger of the two erasure probabilities, and the corner points come from the average probability of each link being active. We show that under certain ratios of the lengths of the modes, these outer-bounds are achievable and thus the capacity region is known. We also discuss the behavior of the inner and outer bounds in other regimes and analyze the gap between the two. One key observation is that coding across the modes is superior to treating each mode as an individual problem.