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 provide a
generic outer bound to the capacity of this system and propose a coding
algorithm that achieves this bound for an arbitrary number of users and
symmetric channel conditions, 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^2/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^2/L) when
each user knows only its own ACK. The proposed algorithms do not require any
prior knowledge of channel statistics.