Multicast Convolutional Network Codes via Local Encoding Kernels

A convolutional network (CN) code can be described by either global encoding kernels (GEKs) or local encoding kernels (LEKs). In the literature, the multicast property of a CN code is described using GEKs, so the design algorithms for multicast CN codes employ GEKs to check this property. For cyclic networks, using GEKs makes the design algorithms time-consuming. In this paper, a new approach is proposed for the design of multicast CN codes for networks with cycles. First, a formula is presented to describe the multicast property using LEKs rather than GEKs. Then, this formula is used to develop a design algorithm for multicast CN codes. This algorithm does not use GEKs, which makes it more efficient than GEK-based algorithms, particularly for large cyclic networks.