  For a two user cooperative orthogonal frequency division multiple access
(OFDMA) system with full channel state information (CSI), we obtain the optimal
power allocation (PA) policies which maximize the rate region achievable by a
channel adaptive implementation of inter-subchannel block Markov superposition
encoding (BMSE), used in conjunction with backwards decoding. We provide the
optimality conditions that need to be satisfied by the powers associated with
the users' codewords and derive the closed form expressions for the optimal
powers. We propose two algorithms that can be used to optimize the powers to
achieve any desired rate pair on the rate region boundary: a projected
subgradient algorithm, and an iterative waterfilling-like algorithm based on
Karush-Kuhn-Tucker (KKT) conditions for optimality, which operates one user at
a time and converges much faster. We observe that, utilization of power control
to take advantage of the diversity offered by the cooperative OFDMA system, not
only leads to a remarkable improvement in achievable rates, but also may help
determine how the subchannels have to be instantaneously allocated to various
tasks in cooperation.
