In this work, we consider incremental redundancy (IR) hybrid automatic repeat request (HARQ), where the transmission rounds are carried over independent block-fading channels. We analyze the multipacket HARQ, where the transmitter allows two different packets to share the same channel block; this stands in contrast with the conventional HARQ, where each packet occupies the entire block. We then optimally assign resources within the block to each packet and in each transmission round. We study superposition coding and time-sharing encoding strategies, and we optimize their parameters to maximize the throughput. Besides the conventional, one-bit (ACK/NACK) signaling we also consider a multibit feedback. We formulate our problem as a Markov decision process (MDP), where the decisions concerning the encoding strategies and their parameters are taken using additional information obtained from the receiver via feedback channel. In the case of the one-bit (ACK/NACK) signaling, the partial state information Markov decision process (PSI-MDP) framework is used to obtain the optimal policies. Numerical examples obtained in a Rayleigh-fading channel indicate that, the proposed multipacket HARQ outperforms the conventional one, by more than 5 dB for high-spectral efficiencies.

In this work we consider incremental redundancy hybrid ARQ (HARQ) transmission of data packets over independent block-fading channels. In HARQ, the transmitter, upon request (NACK), resends the "NACKed" packet in the next available block. Conventionally, the original and retransmitted packets occupy one block, each. In our approach, we allow the transmitter to share the resources between the new and the retransmitted packets. To implement such a multi-packet transmission we consider the superposition coding and the timesharing modulation as possible encoding schemes for simultaneous transmission of both packets. Targeting the maximization of the throughput, we cast the problem into the framework of Markov decision process (MDP), where the decisions about the optimal transmission strategy are taken using information about the state of the receiver in the previous transmissions. Numerical examples obtained in a Rayleigh block-fading channel show that proposed transmission strategy provides notable gains over a conventional HARQ.