Efficient network codes for cyclic networks

In this work we address the problem of network codes for cyclic networks. We show that network codes can be constructed for cyclic networks as long as at least one edge in each cycle has a delay, but it is not required that every edge would have a delay. We then present the algorithm for constructing an optimal multicast network code, developed in our previous work, and analyze its computational complexity, showing that it is polynomial in the graph size. We discuss the properties of the resulting codes, and show the ability to modify the code in a localized manner when sinks are added or removed. This property is also applicable to acyclic networks. Finally, we propose the sequential decoding algorithm we developed in an earlier work for decoding the resulting codes. For this we analyze its decoding delay, for both acyclic and cyclic networks