Beyond Routing: An Algebraic Approach to Network Coding

Abstract— In this paper we consider the issue of network capacity. The recent work by Li and Yeung examined the network capacity of multicast networks and related capacity to cutsets. Capacity is achieved by coding over a network. We present a new framework for studying networks and their capacity. Our framework, based on algebraic methods, is surprisingly simple and effective. For networks which are restricted to using linear codes (we make precise later the meaning of linear codes, since the codes are not bit-wise linear), we find necessary and sufficient conditions for any given set of connections to be achievable over a given network. For multicast connections, linear codes are not a restrictive assumption, since all achievable connections can be achieved using linear codes. Moreover, coding can be used to maintain connections after permanent failures such as the removal of an edge from the network. We show necessary and sufficient conditions for a set of connections to be rob...

• Type: Conference
• Year: 2002
• Where: INFOCOM
• Authors: Muriel Médard, Ralf Koetter
• Keywords: Communications, INFOCOM 2002, Linear Codes, Multicast Connection, Network Capacity