The Broadcast Channel With Degraded Message Sets and Unreliable Conference - Itzhak, Dor; Steinberg, Yossef (IEEE transactions on information theory, 2021)
It has long been observed that cooperation between users in a communication network can improve its performance. Unfortunately, in practical ad-hoc networks, cooperation links can be unreliable, and in many cases part of the users in the system cannot be updated about their availability. In such a case we need robust coding schemes that exploit the cooperation links if they are present, but can still operate if cooperation is not possible. In this work we study the general broadcast channel with degraded message sets and cooperation link that may be absent, and derive its capacity region under such uncertainty conditions. A generalization of this model is studied, where the cooperation link capacity is one of k possible values, and its capacity region is derived. We examine the situation where the cooperation link capacity is random and suggest the following performance criterion: maximize the average rate of one user, subject to a constraint on the rate of the other user and the requirement that the system will operate in any realization of the (random) cooperation link. As examples to illustrate our results, the Gaussian broadcast channel is extensively examined, and its capacity is derived for the various cooperation models and assumptions suggested throughout.