  A point-to-point discrete-time scheduling problem of transmitting $B$
information bits within $T$ hard delay deadline slots is considered assuming
that the underlying energy-bit cost function is a convex monomial. The
scheduling objective is to minimize the expected energy expenditure while
satisfying the deadline constraint based on information about the unserved
bits, channel state/statistics, and the remaining time slots to the deadline.
At each time slot, the scheduling decision is made without knowledge of future
channel state, and thus there is a tension between serving many bits when the
current channel is good versus leaving too many bits for the deadline. Under
the assumption that no other packet is scheduled concurrently and no outage is
allowed, we derive the optimal scheduling policy. Furthermore, we also
investigate the dual problem of maximizing the number of transmitted bits over
$T$ time slots when subject to an energy constraint.
