Unified construction algorithm of network coding in cyclic networks

Network coding in cyclic networks may have better performance than network coding in acyclic networks with regard to the multi-unicast scenarios. Harvey et al. showed that network coding in cyclic networks can be strictly better than fractional routing in conservative networks which have widely practical scenarios such as P2P networks. Hence, we motivated investigating how to achieve that better performance of network coding in cyclic networks by a general construction algorithm. Li et al. presented there are four levels for network code in cyclic networks, including Basic Convolutional Network Code(BCNC), Convolutional Dispersion(CD), Convolutional Broadcast(CB) and Convolutional Multicast(CM). Subsequently, it is interesting to investigate how to construct all four levels of network coding in cyclic networks. Based on our previous work of construction algorithm of BCNC, we proposed a unified algorithm to construct network coding in cyclic networks using notion of flow set. Our contributions were as follows:(1)we showed insights of the essential difference between two classes(i.e. BCNC and CD/CB/CM) of network codes in cyclic networks. (2)we showed insights how to uniformly handle cycles for these two classes of network codes in cyclic networks by proposing the unified construction algorithm. Here, we used the cycles classifications defined by Barbero et al., including link cycles but flow-acyclic, simple flow cycles and flow knots(simply knots).