Submodular Rate Region Models for Multicast Communication in Wireless Networks by Maximilian Riemensberger

Author:Maximilian Riemensberger
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

We remark that another, rather trivial necessary and sufficient condition directly follows from the definition of mutual information. This condition is that

(4.50)

is submodular if and only if the conditional entropy is supermodular as a function of . This condition is especially useful for erasure networks since the entropy can easily be obtained for such networks.

4.2.2 Noisy Network Coding Inner Bound

In this section, we apply the noisy network coding scheme to networks of independent broadcast channels. Although the structure of such networks leads to a cut-set outer bound that decomposes across all nodes as shown in Sect. 4.2.1, the noisy network coding inner bound does not always admit such a decomposition due to the joint quantization of of all channel outputs at each receiver node and possible dependencies across the outputs of each broadcast channel. The per-terminal cut rate region that generates the noisy network coding inner bound for a network of independent broadcast channels is given by

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