On Static Code Construction for Alternating Multicast and Simultaneous Multicasts

In this paper, we introduce a network multicast problem called the alternating multicast problem. In this problem, there is more than one multicast on the network, but only one of the multicasts can take place at any time. We propose an algorithm for constructing a linear network code which is static in the sense that the coding operations do not depend on the multicast. The code so constructed achieves the max-flow bound for each multicast, i.e., optimality is achieved when the base field is sufficiently large. An upper bound on the required field size for constructing the code is also obtained. We conjecture that a network code constructed by our algorithm can be converted into a network code for the associated simultaneous multicast problem, i.e., all the multicasts can take place at the same time. An example is presented to illustrate our conjecture.