On Fading Broadcast Channels with Channel Output Feedback

The Broadcast Channel (BC) has been widely used as a downlink communication system model. One of particularly important BCs is the Fading Additive White Gaussian Noise Broadcast Channel (F-AWGN-BC), under various types of the Channel State Information (CSI) like perfect CSI at both the transmitter (CSIT) and receiver (CSIR), at the receiver only, or delayed CSI at the transmitter. Despite the considerable progress on the capacity region of the BC in the absence of fading, the capacity region of the AWGN-BC with fading remains open when the CSI is not available at the transmitter. This dissertation defense will apply techniques from information theory, control theory, and deep learning to investigate the benefits of feedback in improving fundamental limits on information flow in fading BCs. We consider two channel models: the Layered Packet Erasure Broadcast Channel (LPE-BC) and Fading Additive White Gaussian Noise Broadcast Channel (F-AWGN-BC). The first model is used to characterize channel fading and is an approximation of the second one. We focus on the case where the receiver has perfect and instantaneous CSI, and the transmitter obtains the one-unit-delayed received message along with the CSI through the noiseless feedback link. The major contributions are summarized as follows: 1) Deriving inner and outer bounds to the capacity region of the fading BCs with COF; 2) Identifying the stability region for the LPE-BC with COF; 3) Designing coding mechanisms by incorporating control/estimation theory and deep learning. These techniques serve as building blocks for understanding the capacity region of wireless communication systems and developing coding methods for high reliability, low power, and broad communication.