Network Coding in a Multicast Switch

TL;DR

This paper demonstrates that intra-flow network coding in multicast switches enlarges the achievable rate region, simplifies throughput characterization, and can replace hardware speedup with software-based coding, improving switch performance.

Contribution

It introduces a graph-theoretic characterization of the rate region using the enhanced conflict graph and proposes both offline and online scheduling algorithms leveraging network coding.

Findings

Network coding enlarges the rate region for multicast switches.

A simple graph-theoretic characterization of the rate region is provided.

Coding can replace hardware speedup in switch throughput enhancement.

Abstract

The problem of serving multicast flows in a crossbar switch is considered. Intra-flow linear network coding is shown to achieve a larger rate region than the case without coding. A traffic pattern is presented which is achievable with coding but requires a switch speedup when coding is not allowed. The rate region with coding can be characterized in a simple graph-theoretic manner, in terms of the stable set polytope of the "enhanced conflict graph". No such graph-theoretic characterization is known for the case of fanout splitting without coding. The minimum speedup needed to achieve 100% throughput with coding is shown to be upper bounded by the imperfection ratio of the enhanced conflict graph. When applied to KxN switches with unicasts and broadcasts only, this gives a bound of min{(2K-1)/K,2N/(N+1)} on the speedup. This shows that speedup, which is usually implemented in hardware, can often be substituted by network coding, which can be done in software. Computing an offline schedule (using prior knowledge of the flow rates) is reduced to fractional weighted graph coloring. A graph-theoretic online scheduling algorithm (using only queue occupancy information) is also proposed, that stabilizes the queues for all rates within the rate region.