Multicast streaming codes (Mu-SCo) for burst erasure channels

Streaming codes sequentially encode the source stream and reproduce each source packet with a fixed delay. We study multicast streaming codes (MU-SCo) that simultaneously serve two users : one user, whose channel introduces a burst-erasure length of B₁ and tolerates a delay of T₁ and a second user, whose channel introduces a burst-erasure length of B₂ and tolerates a delay of T₂. We show that the streaming capacity intricately depends on the burst-delay parameters and provide explicit constructions that attain the capacity for a wide range of parameters. In particular we identify regimes where (a) avoiding interference between the parity checks of the two users is optimal (b) the weaker user treats parity checks of the stronger user as side information to decode part of the source stream and (c) the capacity is achieved by a single user code. Our results shed new insights into the role of delay on user ordering in broadcast channels.