Coding schemes for broadcast erasure channels with feedback: the two multicast case

We 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 [1], [2], we 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, we 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. We finally provide, through an information-theoretic analysis, sufficient but not necessary asymptotic conditions between $N$ and $n$ (the number of transmissions) for which the achieved sum rate, under \textit{any} coding scheme, is essentially identical to that of timesharing.