@MISC{Vasudevan_onbroadcast, author = {Dinkar Vasudevan and Satish Babu Korada}, title = {On Broadcast with a Common Message over Networks}, year = {} }

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Abstract

We consider the following communication problem over a directed graph. A source node wants to transmit a common message to a set of receiver nodes along with a private message to each of the receivers. We show a class of networks for which the achievable rate region is given by the cut-set bounds. From the cut-set bounds, we get R o to be an outer bound to the rate region R (R ⊆ R o). For the case K = 2, it was shown in [1],[6],[5] that the cut-set bound is tight. It was observed in [4] that the cut-set bound is not necessarily tight when K> 2. The authors provide the example of the network in Figure 1. The network does not support the rate point (1, 0, 1, 0) even though it lies in R o. The authors also demonstrate achievable rates by combining the technique of network coding and linear precoding at the source. In this work, we show a class of networks for which the cut-set bound is tight. This class consists of all acyclic networks for which the min-cuts are characters t1 t2 t3 Figure 1: Network for which the cut-set bound is not tight. All links have unit capacity. 1.