An efficient basic convolutional network code construction algorithm on cyclic networks

Similar to acyclic networks, over cyclic networks, there also exist four classes of optimal convolutional network codes, which are referred to as basic convolutional network code (BCNC), convolutional dispersion (CD), convolutional broadcast (CB), and convolutional multicast (CM), respectively. And from the perspective of linear independence among the global encoding kernels (GEKs), BCNC is with the best strength. In this paper, we present an efficient construction algorithm for BCNC over cyclic networks. Our algorithm can positively provide the maximal required cardinality of the local encoding kernels (LEKs). Another advantage of this algorithm is that for an existing code, when some non-source nodes and associated edges are added, our algorithm can correspondingly modify the already assigned LEKs in a localized manner. And we can just reset the LEKs along some special flow paths educed by the added nodes and edges, rather than reconstructing the whole code in its expanding network.