  We consider the $N$-user broadcast erasure channel with $N$ unicast sessions
(one for each user) where receiver feedback is regularly sent to the
transmitter in the form of ACK/NACK messages. We first provide a generic outer
bound to the capacity of this system; we then propose a virtual-queue-based
inter-session mixing coding algorithm, determine its rate 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 that asymptotically differs from the outer bound by 1
bit as $L\to \infty$, where $L$ is the number of bits per packet (packet
length). For the case of arbitrary channel statistics, we present a
modification of the previous algorithm whose rate region is identical to the
outer bound for N=3, when instant feedback is known to all users, and differs
from the bound by 1 bit as $L\to \infty$, when the 3 users know only their own
ACK. The proposed algorithms do not require any prior knowledge of channel
statistics.
