# RC-LDPC-Polar Codes for Information Reconciliation in Continuous-Variable Quantum Key Distribution

## TL;DR

This paper introduces a new coding method to improve error correction in quantum key distribution, especially under unstable signal conditions.

## Contribution

The novel RC-LDPC-Polar code combines LDPC and polar coding for better performance in quantum key reconciliation.

## Key findings

- The RC-LDPC-Polar code achieves a lower error rate under varying SNR conditions.
- The proposed scheme increases the final key rate and extends transmission distance in CV-QKD.

## Abstract

Continuous-variable quantum key distribution faces significant challenges, including quantum channel instability, particularly fluctuations in the signal-to-noise ratio (SNR) and extremely low SNR scenarios. Furthermore, non-ideal polar codes, characterized by insufficient polarization in finite-length regimes, can lead to some sub-channels being neither completely noise-free nor fully noise-dominated. This phenomenon limits the error correction capability when such codes are applied to information reconciliation. To address these challenges, we propose a novel RC-LDPC-Polar code for the CV-QKD reconciliation algorithm. We combine the error resilience of LDPC codes with the efficiency advantages of polar coding. This scheme supports adaptive rate adjustment across varying SNR conditions. Our simulation experiments demonstrate that the RC-LDPC-Polar concatenated coding scheme achieves a lower error rate under varying SNR conditions. Meanwhile, the proposed scheme achieves a higher final key rate and a longer transmission distance.