On the Shannon capacity and queueing stability of random access multicast

TL;DR

This paper compares the Shannon capacity and queueing stability in multicast random access systems, showing that certain coding policies can outperform retransmissions and that capacity bounds do not always match stability regions.

Contribution

It characterizes the Shannon capacity and stable throughput regions under different policies, revealing new insights into their relationship and challenging existing conjectures.

Findings

Random linear coding achieves higher stable throughput than retransmission.

Shannon capacity region can strictly outer bound the stable throughput region.

Results challenge the conjecture that capacity and stability regions always coincide.

Abstract

We study and compare the Shannon capacity region and the stable throughput region for a random access system in which source nodes multicast their messages to multiple destination nodes. Under an erasure channel model which accounts for interference and allows for multipacket reception, we first characterize the Shannon capacity region. We then consider a queueing-theoretic formulation and characterize the stable throughput region for two different transmission policies: a retransmission policy and random linear coding. Our results indicate that for large blocklengths, the random linear coding policy provides a higher stable throughput than the retransmission policy. Furthermore, our results provide an example of a transmission policy for which the Shannon capacity region strictly outer bounds the stable throughput region, which contradicts an unproven conjecture that the Shannon capacity and stable throughput coincide for random access systems.