Fault Tolerant Network Coding

Consider a communication network in which a source node wishes to multicast information to some sink nodes on the network. In the traditional setting, every node can only pass on the data it receives from incoming links to the links leaving it. We consider an extended setting which gives the intermediate nodes more “power”. In our model, each node may send any linear combination of the received data on the outgoing links. Such protocols, known as Linear Network Coding schemes, have been proved to guarantee optimal multicast throughput (that is, the maximum number of different data packets the source can transmit to all the sinks in one execution of the protocol matches the theoretical bound). In this work, we address the problem of fault tolerance in network coding. More specifically, we are interested in obtaining reliable coding schemes which guarantee optimal (in a sense we shall explain later) throughput even when some edges stop functioning, or are corrupt by noise. We modify an existing algorithm to provide a centralized scheme for finding such codes that tolerate any failure pattern from a polynomially bounded set of possible failure patterns in a network. A failure pattern is a set of edges that fail (transmits a zero message). When an edge fails, it is assumed to fail throughout the execution of the protocol. Our algorithm is rate optimal in the asymptotic limit with respect to the message packet size, in the sense that it sustains a flow rate equal to the minimum of the max-flows from the source to the sinks with the failed edges being deleted. Such codes could be utilized in networks where certain edges are prone to failure, and yet optimal throughput is expected regardless of the edges failing. We also present simple extensions which optimally tolerate corruption of edges by white noise (they transmit a purely random message).