The main objective of this study is to investigate the structures and procedures which are promising to achieve higher rates and larger rate regions in the relay channels and the communication networks that contain relay nodes. In particular, the study places particular emphasis on the relaying techniques pertaining to compress-and-forward.
The thesis first examines a generalization of decode-and-forward (DF) and compress-and-forward (CF) in Gaussian channels. Although this generalization has been known for over thirty years, the result in this thesis is the first to illustrate the signal-to-noise ratio (SNR) regions in which the generalization reduces to constituent DF or CF schemes. In particular, the thesis demonstrates the existence of SNR regions in which the generalization is guaranteed to supersede both DF and CF, but with a gain of within 0.5 bits per channel use.
Having gained insight into the random binning in the CF scheme, this thesis argues that a new decoding procedure exploiting the N-to-1 mapping based on binning is able to relax the rate constraint on the relay transmission, and generalize the noisy network coding based schemes which are constrained to the 1-to-1 mapping. This thesis identifies two instances in which exploiting the N-to-1 mapping inherent in this generalization yields rate gains, even though it does not yield such a gain in other multimessage networks.
In the analysis of a secure communication problem, the thesis introduces the concept of “friendly” eavesdropper in a broadcast channel in the presence of a malicious Gaussian jammer. Taking advantage of the N-to-1 mapping, it is shown that the new decoding procedure enables CF to achieve the capacity of the channel.