Efficient Network Code Design for Cyclic Networks

This paper introduces an efficient polynomial-time code construction algorithm for cyclic networks, which achieves the optimal multicast rate. Until this work, no explicit capacity-achieving polynomial-time code construction for cyclic networks has been known. This new construction algorithm has the additional advantage that as sinks are added or removed from the network, it can modify the existing code in an efficient localized manner, which is beneficial also for acyclic networks. For decoding this code, a polynomial-time sequential decoder for convolutional network codes is also proposed.