Cycle-logical treatment for "Cyclopathic" networks

This correspondence addresses the problem of finding the network encoding equations for error-free networks with multiple sources and sinks. Previous algorithms could not cope with cyclic networks. Networks that are cyclic in three different senses are considered in this correspondence, and two extensions of the polynomial time Linear Information Flow (LIF) algorithm are presented. The first algorithm will produce the network encoding equations for a network which can be cyclic, unless the actual flow paths form cycles. The second algorithm will work also when the flow paths form simple cycles. Finally an example of a third kind of cyclic network, where the previous algorithms will fail, is given. However, a binary encoding is provided also in this case.