Opportunistic Scheduling of Randomly Coded Multicast Transmissions at Half-Duplex Relay Stations

We consider the multicast scheduling problem for the block transmission of packets in a heterogeneous network using a half-duplex relay station (RS). The RS uses random linear coding to efficiently transmit packets over time-varying multicast channels. Our goal is to minimize the average decoding delay. Because of the half-duplex operation, at each time slot, the RS must decide to either: (1) fetch a new packet for encoding from the base station or (2) multicast a coded packet to wireless users. Thus, optimal scheduling hinges on exploiting multicast opportunities while persistently supplying the encoder (at the RS) with new packets. We formulate an associated fluid control problem and show that the optimal policy incorporates opportunism across multicast channels, i.e., the RS performs a multicast transmission only if the collection of channel conditions is favorable; otherwise, it performs a fetch. Based on the fluid policy, we propose an online algorithm. We prove that our algorithm asymptotically incurs no more than 4/3 and 2 times the optimal delay, for two-user and arbitrary number of user system, respectively. Simulation results show that, in fact, our algorithm's performance is very close to theoretical bounds.