  The two-user wireless ergodic fading Broadcast Channel (BC) with partial
Channel State Information at the Transmitter (CSIT) is considered. The CSIT is
given by an arbitrary deterministic function of the channel state. This
characteristic yields a full control over how much state information is
available, from perfect to no information. In literature, capacity derivations
for wireless ergodic fading channels, specifically for fading BCs, mostly rely
on the analysis of channels comprising of parallel sub-channels. This technique
is usually suitable for the cases where perfect state information is available
at the transmitters. In this paper, new arguments are proposed to directly
derive (without resorting to the analysis of parallel channels) capacity bounds
for the two-user fading BC with both common and private messages based on the
existing bounds for the discrete channel. Specifically, a novel approach is
developed to adapt and evaluate the well-known UV-outer bound for the Gaussian
fading channel using the entropy power inequality. Our approach indeed sheds
light on the role of broadcast auxiliaries in the fading channel. It is shown
that the derived outer bound is optimal for the channel with perfect CSIT as
well as for some special cases with partial CSIT. Our outer bound is also
directly applicable to the case without CSIT which has been recently considered
in several papers. Next, the approach is developed to analyze for the fading BC
with secrecy. In the case of perfect CSIT, a full characterization of the
secrecy capacity region is derived for the channel with common and confidential
messages. This result completes a gap in a previous work by Ekrem and Ulukus.
For the channel without common message, the secrecy capacity region is also
derived when the transmitter has access only to the degradedness ordering of
the channel.
