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Power Allocation for Finite-Blocklength IR-HARQ

Wenyu Wang, Minhao Zhu, Kaiming Shen, Zhaorui Wang, Shuguang Cui

TL;DR

The paper tackles energy-efficient power allocation across IR-HARQ rounds in the finite-blocklength regime by deriving a tight upper bound on the outage probability and reformulating the optimization as a geometric program. This bound makes the otherwise intractable problem tractable and guarantees feasibility for the original outage constraint $\mathrm{Pr}_{\mathrm{out}}(M)\le \epsilon$. The resulting GP-based algorithm achieves substantial energy savings compared with fixed-power or infinite-blocklength-based baselines, while meeting stringent reliability targets. The approach offers a practical tool for ultra-reliable, low-latency transmissions in IoT and industrial automation settings.

Abstract

This letter concerns the power allocation across the multiple transmission rounds under the Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ) policy, in pursuit of an energy-efficient way of fulfilling the outage probability target in the finite-blocklength regime. We start by showing that the optimization objective and the constraints of the above power allocation problem all depend upon the outage probability. The main challenge then lies in the fact that the outage probability cannot be written analytically in terms of the power variables. To sidestep this difficulty, we propose a novel upper bound on the outage probability in the finite-blocklength regime, which is much tighter than the existing ones from the literature. Most importantly, by using this upper bound to approximate the outage probability, we can recast the original intractable power allocation problem into a geometric programming (GP) form--which can be efficiently solved by the standard method.

Power Allocation for Finite-Blocklength IR-HARQ

TL;DR

The paper tackles energy-efficient power allocation across IR-HARQ rounds in the finite-blocklength regime by deriving a tight upper bound on the outage probability and reformulating the optimization as a geometric program. This bound makes the otherwise intractable problem tractable and guarantees feasibility for the original outage constraint . The resulting GP-based algorithm achieves substantial energy savings compared with fixed-power or infinite-blocklength-based baselines, while meeting stringent reliability targets. The approach offers a practical tool for ultra-reliable, low-latency transmissions in IoT and industrial automation settings.

Abstract

This letter concerns the power allocation across the multiple transmission rounds under the Incremental Redundancy Hybrid Automatic Repeat reQuest (IR-HARQ) policy, in pursuit of an energy-efficient way of fulfilling the outage probability target in the finite-blocklength regime. We start by showing that the optimization objective and the constraints of the above power allocation problem all depend upon the outage probability. The main challenge then lies in the fact that the outage probability cannot be written analytically in terms of the power variables. To sidestep this difficulty, we propose a novel upper bound on the outage probability in the finite-blocklength regime, which is much tighter than the existing ones from the literature. Most importantly, by using this upper bound to approximate the outage probability, we can recast the original intractable power allocation problem into a geometric programming (GP) form--which can be efficiently solved by the standard method.
Paper Structure (8 sections, 31 equations, 5 figures)

This paper contains 8 sections, 31 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Power Allocation by Bounding and GP
  4. Existing Approximation of Outage Probability
  5. Proposed Approximation of Outage Probability
  6. GP-Based Power Allocation Scheme
  7. Numerical Results
  8. Conclusion

Figures (5)

  • Figure 1: The procedure of the IR-HARQ scheme.
  • Figure 2: Approximations of $\mathrm{Pr}_{\mathrm{out}}(m)$ when $M=5$, $q=40\log(2)\text{ nats}$, $L=50$, $S=5$, and each $p_m=0.8$.
  • Figure 3: Approximation of $\mathrm{Pr}_{\mathrm{out}}(2)$ vs. $S$ when $M=5$, $q=40\log(2)\text{ nats}$, $L=50$, and each $p_m=0.8$.
  • Figure 4: Ultimate outage probability $\mathrm{Pr}_{\mathrm{out}}(M)$ vs. pathloss-to-noise ratio $S$.
  • Figure 5: Per-symbol power consumption $\frac{E}{L}$ vs. pathloss-to-noise ratio $S$.