# Delay-Sensitive NOMA-HARQ for Short Packet Communications
###### Abstract  
This paper investigates the two-user uplink non-orthogonal multiple access (NOMA) paired with the hybrid automatic repeat request (HARQ) in the finite blocklength regime, where the target latency of each user is the priority. To limit the packet delivery delay and avoid packet queuing of the users, we propose a novel NOMA-HARQ approach where the retransmission of each packet is served non-orthogonally with the new packet in the same slot. We use a Markov model (MM) to analyze the dynamics of the uplink NOMA-HARQ with one retransmission and characterize the packet error rate (PER), throughput, and latency performance of each user. We also present numerical optimizations to find the optimal power ratios of each user. Numerical results show that the proposed scheme significantly outperforms the standard NOMA-HARQ in terms of packet delivery delay at the target PER. finite blocklength; HARQ; non-orthogonal multiple access; ultra-reliable and low latency communication +
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regime, e.g., the normal approximation [10]. In particular, the coding gain is reduced at finite blocklengths, as packets experience a finite number of channel observations and the gap to Shannon's limit is increased [6; 10]. To compensate for the coding gain, available diversity sources, such as space and frequency, can be utilized [11; 12]. Due to limited resources and the fact that many URLLC applications will operate over unlicensed bands, frequency diversity is not a viable solution. Instead, one can utilize retransmission techniques, such as hybrid automatic repeat request (HARQ) [13; 14], which increase latency [15; 16]. Non-orthogonal multiple access (NOMA) schemes can be used to exploit channel diversity and resource utilization by simultaneously allocating a channel to multiple users [17]. NOMA has been actively investigated in the past decade, since it can effectively provide higher throughput and flexibility in comparison to orthogonal multiple access (OMA) techniques [7; 18; 19]. In NOMA, multiple devices can share the same radio resources using the superposition of signals. Successive interference cancellation (SIC) is used to separate the signal of each user at the receiver [20]. NOMA can be implemented by either power or code sharing between users [21]. NOMA is mainly analyzed in the asymptotic blocklength regime and, more recently, in the finite blocklength regime, proving that NOMA effectively provides better resource utilization and energy efficiency [22; 23; 24]. In [22; 25], the authors show that NOMA outperforms OMA and reduces the latency under a finite blocklength regime. In NOMA, more users can be served over limited channel resources, resulting in higher spectral efficiency, which reduces latency as well [22]. These features of NOMA make it a potential candidate technique for URLLC and mMTC scenarios. In HARQ, in case of packet failure, the receiver feedbacks a negative acknowledgment (NACK) and requests for retransmission. In contrast, upon receiving an ACK, the transmitter sends a new packet. Upon a retransmission request, the transmitter can either send a duplicate copy of the packet, known as chase combining HARQ (CC-HARQ), or send more redundancy through forward error correcting code, known as incremental redundancy HARQ (IR-HARQ) [26]. The receiver combines the retransmission with failing packets to increase the decoding reliability. With CC-HARQ, maximum ratio combing (MRC) is used to increase the effective signal-to-noise ratio (SNR), whereas with IR-HARQ, code combing is used to increase reliability. In the asymptotic blocklength regime, when the channel is perfectly known at the transmitter, rate adaptation via adaptive modulation and coding can be used to reduce the retransmission requests [27]. However, in the finite blocklength regime, the retransmission requests are more probable due to the high error rate of finite length codes [28]. Both IR-HARQ and CC-HARQ are actively being investigated in the finite blocklength regime [13; 15].