Constructing Network Coding in Cyclic Networks with the Best Linear Independence

Capacity of network coding in cyclic networks can be strictly better than routing. Harvey et al. showed that it exists in the practical scenarios such as the widespread P2P networks. Thus, it is of application significance to investigate how to construct network code in cyclic networks. According to Li et al., there are four levels of network code in cyclic networks, including convolutional multicast (CM), convolutional broadcast (CB), convolutional dispersion (CD), and basic convolutional network code (BCNC). This paper focuses on the BCNC that is with the best linear independence, which means it can provide the most efficient transmission in that it has the minimum redundance. The contributions of this paper are (1) to improve our previous BCNC algorithm; (2) to show insights of the essential difference between BCNC and CM/CB/CD which is of great theoretical significance to understand how different kinds of cycles affect the network coding construction.