Results on the broadcast channels
- The broadcast channel, first studied by Tom Cover, is a model for one-to-many communications, such as the downlink of a cellular system. The capacity region of this channel, defined as the closure of the set of all achievable rate tuples, characterizes the optimal tradeoff among simultaneously achievable data rates. Inner and outer bounds on the capacity region have been obtained, but they coincide only under certain conditions, and the capacity region in general remains unknown. This dissertation establishes new capacity results for broadcast channels with and without feedback. First, we simplify the superposition coding inner bound and establish new optimality results for the superposition coding inner bound for a 2-receiver discrete memoryless broadcast channel. Second, we show that the capacity region of the continuous-time Poisson broadcast channel is achieved via superposition coding for most channel parameter values. Interestingly, the channel in some subset of these parameter values does not belong to any of the existing classes of broadcast channels for which superposition coding is optimal. For the rest of the channel parameter values, we show that there is a gap between the best known inner and outer bounds, namely, Marton's inner bound and the Nair--El Gamal outer bound. Third, we establish the capacity region of several classes of broadcast channels with random state, in which the channel to each user is selected from two possible channel state components and the state is known only at the receivers. Some classes of broadcast channels for which we establish the capacity region do not belong to any class of broadcast channels for which the capacity region was previously known. Last, we show that the Maddah-Ali--Tse scheme, which establishes the symmetric capacity of two example broadcast channels with strictly causal state information at the transmitter, is a simple special case of the Shayevitz--Wigger scheme for the broadcast channel with generalized feedback. We then introduce a new broadcast channel example that shares many features with the Maddah-Ali--Tse examples, for which we show that another special case of Shayevitz-Wigger scheme attains a higher symmetric rate than the MAT scheme. The symmetric capacity of this example is not known, however. The combined results of this work shed light on our understanding of broadcast channels, and the tools and intuition developed during the research could also be applied to other network information theory problems.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Kim, Hye ji
|Stanford University, Department of Electrical Engineering.
|El Gamal, Abbas A
|El Gamal, Abbas A
|Statement of responsibility
|Hye ji Kim.
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Hye ji Kim
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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