We consider the N-user broadcast erasure channel where feedback from the users is fed back to the transmitter in the form of ACK messages. We first provide a generic outer bound to the capacity of this system; we then propose a coding algorithm, compute its throughput region and show that it achieves capacity under certain conditions on channel statistics, assuming that instantaneous feedback is known to all users. Removing this assumption results in a rate region which differs from the outer bound by a factor O(N/L), where L is packet length. For the case of non-symmetric channels, we present a modification of the previous algorithm whose achievable region is identical to the outer bound for N 3, when instant feedback is known to all users, and differs from the bound by O(N/L) when each user knows only its own ACK. The proposed algorithms do not require any prior knowledge of channel statistics.