The Broadcast Channel With Degraded Message Sets and Unreliable Conference

• Published in: IEEE transactions on information theory Vol. 67; no. 9; pp. 5623 - 5650
• Main Authors: Itzhak, Dor, Steinberg, Yossef
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ad hoc networks; Alliances; Broadcast channels; Broadcasting; Communication networks; conferencing decoders; Cooperation; Decoding; degraded message sets; Encoding; Indexes; Receivers; Relays; Uncertainty; unreliable cooperation
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3091779

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 <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> 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.