HARQ-IR Aided Short Packet Communications: BLER Analysis and Throughput Maximization

TL;DR

This paper tackles reliable, low-latency short-packet communications by analyzing average BLER under HARQ-IR with finite-blocklength constraints. It introduces three numerical approaches—trapezoidal approximation, Gauss–Laguerre quadrature (enhanced by dynamic programming), and an asymptotic high-SNR method—to compute the average BLER with correlated decoding events, enabling LTAT optimization. For throughput maximization, the authors develop a GP-based solution using the asymptotic BLER and a DRL-based constrained MDP (via DDPG) to learn power allocations, complemented by a truncation-based update strategy for stability. Numerical results show DRL outperforms GP at low SNR, while GP remains attractive at high SNR due to lower complexity, providing a practical trade-off for HARQ-IR in next-generation networks.

Abstract

This paper introduces hybrid automatic repeat request with incremental redundancy (HARQ-IR) to boost the reliability of short packet communications. The finite blocklength information theory and correlated decoding events tremendously preclude the analysis of average block error rate (BLER). Fortunately, the recursive form of average BLER motivates us to calculate its value through the trapezoidal approximation and Gauss-Laguerre quadrature. Moreover, the asymptotic analysis is performed to derive a simple expression for the average BLER at high signal-to-noise ratio (SNR). Then, we study the maximization of long term average throughput (LTAT) via power allocation meanwhile ensuring the power and the BLER constraints. For tractability, the asymptotic BLER is employed to solve the problem through geometric programming (GP). However, the GP-based solution underestimates the LTAT at low SNR due to a large approximation error in this case. Alternatively, we also develop a deep reinforcement learning (DRL)-based framework to learn power allocation policy. In particular, the optimization problem is transformed into a constrained Markov decision process, which is solved by integrating deep deterministic policy gradient (DDPG) with subgradient method. The numerical results finally demonstrate that the DRL-based method outperforms the GP-based one at low SNR, albeit at the cost of increasing computational burden.

Figures (10)

• Figure 1: An example of HARQ-IR aided short packet communications with $M=3$.
• Figure 2: Computational procedure of trapezoidal approximation.
• Figure 3: The DDPG network for power allocation of HARQ-IR-aided short packet communications.
• Figure 4: The average BLER $\mathbb {\bar{P}}_M$ versus the average SNR $\bar{\gamma}$.
• Figure 5: The average BLER $\mathbb {\bar{P}}_M$ versus the maximum number of transmissions $M$.

Theorems & Definitions (6)

• Corollary 1
• proof
• Lemma 1
• proof : Proof
• Theorem 1
• proof