On the Queueing Performance of HARQ Systems with Coding over Finite Transport Blocks

With the growing popularity of mobile applications such as voice over IP (VoIP) and real-time conversational video, and due to the scarcity of the available radio spectrum, increasing the spectral efficiency of wireless systems under quality of service (QoS) constraints becomes increasingly important. Accordingly, in this paper we investigate the maximum achievable rate of incremental redundancy type hybrid automatic repeat request (IR-HARQ) over the Rayleigh fading channel under probability of error, and queueing delay violation probability constraints, in the finite code blocklength regime. We model the Rayleigh fading channel by a finite-state Markov channel (FSMC) where the channel in each state is modeled as additive white Gaussian noise (AWGN). We derive the dispersion of parallel AWGN channels with finite input alphabets (e.g. pulse amplitude modulation (PAM)), which is used to track the operation of IR-HARQ over the wireless channel for a given modulation scheme, and coding rate. We then use a two-dimensional Markov process tracking the time evolution of a queueing system, where data packets arriving at the queue are transmitted over the wireless channel with IR-HARQ. This Markov process is used to derive an upper bound on the queueing delay violation probability and to jointly approximate the average rate and the average probability of error of HARQ as a function of the modulation scheme and the coding rate. Finally, we present numerical results.