We investigate reliable data packet delivery employing random linear packet coding for a half-duplex underwater acoustic link. Packet coding is performed on a group of M information-bearing packets so as to form N\geq M coded packets, where N is chosen such that a pre-specified probability of successful decoding is maintained at the receiver. We regard a group of N coded packets as one super-packet, on which we apply an ARQ technique. Specifically, we group L super-packets and apply a group stop-and-wait acknowledgment procedure to the so-obtained unit (a super-group) to achieve full reliability. We also explore adaptive power and rate control combined with the proposed technique in order to improve the performance on fading channels. Using the channel gain information obtained via feedback from the receiver, the transmitter adjusts its power and coding rate such that the average energy per bit is minimized. In doing so, two constraints are observed, one on the maximum transmit power and another on the size N of the super-packet. Under these constraints, we develop the adaptation policy and provide analytical results for the throughput efficiency. Finally, we compare the performance of the proposed technique to that of conventional stop-and-wait, as well as a full-duplex benchmark, showing that packet coding technique on a half-duplex link can achieve a throughput efficiency that is very close to that of a full-duplex link.