Rate-Compatible Polar- and LDPC-Coded Hybrid ARQ Aided Reverse Reconciliation in CV-QKD

Continuous-variable quantum key distribution (CV-QKD) systems face challenges in maintaining efficient reconciliation over long distances due to the time variant signal-to-noise ratio (SNR) imposed by channel quality fluctuations. Hence fixed-rate error-correction schemes using low-density parity-check (LDPC) or Polar codes lead to high block-error rates (BLER) and degraded secret key rates (SKR). To overcome this, we propose an incremental redundancy aided hybrid automatic repeat request (IR-HARQ) protocol using rate-compatible Polar and LDPC codes. Explicitly, by puncturing a mother code and progressively transmitting additional redundant bits, our method dynamically adapts the effective coding rate to the prevalent channel conditions, achieving 2–3 dB SNR gains per retransmission. This adaptive strategy avoids unnecessary redundancy in good channels and strengthens protection in poor channels, thereby improving reconciliation efficiency. Simulation results show that our IR-HARQ scheme significantly enhances the BLER, throughput, and secure transmission distance compared with single-transmission schemes. Moreover, our study highlights that Polar IR-HARQ achieves superior performance in short block-length and low-SNR scenarios, while LDPC IR-HARQ is more competitive for longer codes and higher SNR. These findings confirm IR-HARQ as an attractive and versatile reconciliation solution for real-world CV-QKD deployments.