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The authors consider the single hop broadcast packet erasure channel (BPEC) with two multicast sessions (each of them destined to a different group of N users) and regularly available instantaneous receiver ACK/NACK feedback. Using the insight gained from recent work on BPEC with unicast and degraded messages,, they propose a virtual queue based session-mixing algorithm, which does not rely on knowledge of channel statistics and achieves capacity for N = 2 and iid erasures. Since the optimal extension of this algorithm to N > 2 is not straightforward, they then describe a low complexity algorithm which outperforms standard timesharing for arbitrary N and is actually asymptotically better than timesharing, for any finite N, as the erasure probability goes to zero.
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