  We analyze the opportunistic relaying based on HARQ transmission over the
block-fading channel with absence of channel state information (CSI) at the
transmitter nodes. We assume that both the source and the relay are allowed to
vary their transmission rate between the HARQ transmission rounds. We solve the
problem of throughput maximization with respect to the transmission rates using
double-recursive Dynamic Programming. Simplifications are also proposed to
diminish the complexity of the optimization. The numerical results confirm that
the variable-rate HARQ can increase the throughput significantly comparing to
its fixed-rate counterpart.
