Ralf Koetter

The benefits of coding over routing in a randomized setting

A novel randomized network coding approach for robust, distributed transmission and compression of information in networks is presented, and its advantages over routing-based approaches is demonstrated.

Byzantine modification detection in multicast networks using randomized network coding

Distributed randomized network coding, a robust approach to multicasting in distributed network settings, can be extended to provide Byzantine modification detection without the use of cryptographic functions is presented in this paper.

Beyond routing: an algebraic approach to network coding

We consider the issue of network capacity. 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 the meaning of linear codes precise, 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 robust to a set of permanent failures. For multicast connections, we show the rather surprising result that, if a multicast connection is achievable under different failure scenarios, a single static code can ensure robustness of the connection under all of those failure scenarios.

Linearly representable entropy vectors and their relation to network coding solutions

In this work, we address the following question: “When can we guarantee the optimality of linear coding at all internal nodes of a network?” While sufficient conditions for linear coding throughout the network are known, it is not clear whether relaxing the linearity constraints at the terminal nodes can result in simpler operations at the internal nodes. We present a novel method to analyze the space of network solutions using the constraints resulting from the network topology, and we identify sufficient conditions for an optimal linear solution at all internal nodes. These conditions are also sufficient to characterize the rate region only in terms of Shannon information inequalities.