Classes of Delay-Independent Multimessage Multicast Networks under the Generalized Model

In a network, a node is said to incur a delay if its encoding of each transmitted symbol involves only its received symbols obtained before the time slot in which the transmitted symbol is sent (hence the transmitted symbol sent in a time slot cannot depend on the received symbol obtained in the same time slot). A node is said to incur no delay if its received symbol obtained in a time slot is available for encoding its transmitted symbol sent in the same time slot. Under the classical model, the discrete memoryless multimessage multicast network (MMN) is characterized by one channel and every node in the network incurs a delay. On the other hand, under the generalized model, the MMN can be characterized by multiple channels and some nodes in the network may incur no delay. In this paper, we obtain the capacity regions for three classes of MMN under the generalized model, namely the deterministic network dominated by product distribution, the MMN consisting of independent DMCs and the wireless erasure network. In addition, we show that for any MMN belonging to one of the above three classes, the set of achievable rate tuples under the generalized model and under the classical model are the same, which implies that the set of achievable rate tuples for the MMN does not depend on the amount of delay incurred by each node in the network. Index Terms capacity region, classical model, delay-independent, generalized model, multimessage multicast network (MMN).