  This paper investigates the problem of energy-efficient packet transmission
with arbitrary arrival instants and deadline constraints over a point-to-point
Additive White Gaussian Noise (AWGN) channel. This is different from previous
work where it is assumed that the packets follow a First-In-First-Out (FIFO)
order in that the packets that arrive earlier will have a deadline that is also
earlier. We first investigate the necessary and sufficient conditions of the
optimal transmission scheduler. We then propose an algorithm which finds the
transmission schedule of each packet in the order of the packets with the
largest transmission rate to the packets with the smallest transmission rate.
Finally, we show that our algorithm satisfies the sufficient conditions of the
optimal transmission scheduler and thus, is optimal.
