Stable Throughput for Multicast With Random Linear Coding

This paper compares scheduling and coding strategies for a multicast version of a classic downlink problem. We consider scheduling strategies where, in each time slot, a scheduler observes the lengths of all queues and the connectivities of all links and can transmit the head-of-the-line packet from a single queue. We juxtapose this to a coding strategy that is simply a form of classical random linear coding. We show that there are configurations for which the stable throughput region of the scheduling strategy is a strict subset of the corresponding throughput region of the coding strategy. This analysis is performed for both time-invariant and time-varying channels. The analysis is also performed both with and without accounting for the impact on throughput of including coding overhead symbols in each encoded packet. Additionally, we compare coding strategies that only code within individual queues against a coding strategy that codes across separate queues. The strategy that codes across queues simply sends packets from all queues to all receivers. As a result, this strategy sends many packets to unnecessary recipients. We show, surprisingly, that there are cases where the strategy that codes across queues can achieve the same throughput region achievable by coding within individual queues.