  In this paper, fading Gaussian multiuser channels are considered. If the
channel is perfectly known to the transmitter, capacity has been established
for many cases in which the channels may satisfy certain information theoretic
orders such as degradedness or strong/very strong interference. Here, we study
the case when only the statistics of the channels are known at the transmitter
which is an open problem in general. The main contribution of this paper is the
following: First, we introduce a framework to classify random fading channels
based on their joint distributions by leveraging three schemes: maximal
coupling, coupling, and copulas. The underlying spirit of all scheme is, we
obtain an equivalent channel by changing the joint distribution in such a way
that it now satisfies a certain information theoretic order while ensuring that
the marginal distributions of the channels to the different users are not
changed. The construction of this equivalent multi-user channel allows us to
directly make use of existing capacity results, which includes Gaussian
interference channels, Gaussian broadcast channels, and Gaussian wiretap
channels. We also extend the framework to channels with a specific memory
structure, namely, channels with finite-state, wherein the Markov fading
broadcast channel is discussed as a special case. Several practical examples
such as Rayleigh fading and Nakagami-\textit{m} fading illustrate the
applicability of the derived results.
