Network Coding in a Multicast Switch

TL;DR

This paper demonstrates that network coding in multicast switches enhances throughput, simplifies rate region characterization, and enables online scheduling algorithms that stabilize queues without switch speedup.

Contribution

It introduces a graph-theoretic framework for multicast switch rate regions with coding, and develops online algorithms based on stable set computations.

Findings

Network coding enlarges the rate region in multicast switches.

Coding eliminates the need for switch speedup in certain traffic patterns.

A maximum weighted stable set algorithm stabilizes queues within the rate region.

Abstract

We consider the problem of serving multicast flows in a crossbar switch. We show that linear network coding across packets of a flow can sustain traffic patterns that cannot be served if network coding were not allowed. Thus, network coding leads to a larger rate region in a multicast crossbar switch. We demonstrate a traffic pattern which requires a switch speedup if coding is not allowed, whereas, with coding the speedup requirement is eliminated completely. In addition to throughput benefits, coding simplifies the characterization of the rate region. We give a graph-theoretic characterization of the rate region with fanout splitting and intra-flow coding, in terms of the stable set polytope of the 'enhanced conflict graph' of the traffic pattern. Such a formulation is not known in the case of fanout splitting without coding. We show that computing the offline schedule (i.e. using prior knowledge of the flow arrival rates) can be reduced to certain graph coloring problems. Finally, we propose online algorithms (i.e. using only the current queue occupancy information) for multicast scheduling based on our graph-theoretic formulation. In particular, we show that a maximum weighted stable set algorithm stabilizes the queues for all rates within the rate region.