  We provide the solution for optimizing the power and resource allocation over
block-fading relay-assisted broadcast channels in order to maximize the long
term average achievable rates region of the users. The problem formulation
assumes regenerative (repetition coding) decode-and-forward (DF) relaying
strategy, long-term average total transmitted power constraint, orthogonal
multiplexing of the users messages within the channel blocks, possibility to
use a direct transmission (DT) mode from the base station to the user terminal
directly or a relaying (DF) transmission mode, and partial channel state
information. We show that our optimization problem can be transformed into an
equivalent "no-relaying" broadcast channel optimization problem with each
actual user substituted by two virtual users having different channel qualities
and multiplexing weights. The proposed power and resource allocation strategies
are expressed in closed-form that can be applied practically in centralized
relay-assisted wireless networks. Furthermore, we show by numerical examples
that our scheme enlarges the achievable rates region significantly.
