Multipacket Hybrid ARQ: Closing Gap to the Ergodic Capacity

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.