Increased-Efficiency Multiple-Decoding-Attempts Error Correction for Continuous-Variable Quantum Key Distribution

TL;DR

This work addresses the CV-QKD information reconciliation bottleneck by formalizing multiple-decoding-attempt (MDA) protocols and evaluating two rate-lowering strategies. It compares bit-revelation based MDA_a with RL-LDPC-based MDA_b, demonstrating that rate-adaptation via RL-LDPC codes yields larger secret-key fractions (SKF) and substantial FER reductions in simulations across two scenarios, while keeping leakage within manageable bounds. Decoding complexity is analyzed through average iterations and an LDPC-aware metric, showing that MDA_b can outperform MDA_a with only modest or even negligible added complexity when using LLR-inheritance. Overall, the results indicate that true rate-adaptive MDA with RL-LDPC codes can notably enhance CV-QKD performance under fluctuating channel conditions, offering a practical path to higher SKR over longer distances.

Abstract

In continuous-variable quantum key distribution (CV-QKD), the performance of the information reconciliation (IR) step is critical for the achievable secret key rate (SKR) and transmission distance. We show how to improve on the recently introduced implementation of an IR-protocol involving multiple decoding attempts (MDA) and validate the method on simulated data in different application scenarios. Throughout, we demonstrate meaningful SKR-gains compared to both the standard protocol of a single decoding attempt and to the original MDA-implementation, even at given decoding complexity.

Figures (6)

• Figure 1: Single decoding attempt: Frame error rate (FER) and asymptotic secret key fraction (SKF) (with the RL-LDPC code of ecc with the fixed choice of $r=0.02$) on frames simulated for a range of SNR-values. The asymptotic SKF is shown for the two choices of the modulation variance $V_A$ considered, resulting in i) a high and ii) a low value of $\text{FER}_*$ (white color markers), respectively.
• Figure 2:
• Figure 3: Example ii): $\text{FER}_* \ll 1$ ($V_A=0.5$): Secret key fraction (SKF) after the second decoding attempt (DA) depending on the choices of code rate for either of the DAs. The best possible result of a single decoding attempt (SDA) is shown as a reference.
• Figure 4: Performance and complexity: SKF achieved by the various schemes versus the average number of decoding iterations used, $\overline{l}$, and the average allowed number of decoding iterations, $\overline{D}$ (see Eq. \ref{['DBar']}), respectively. The plotted points result from a variation of $l_{\textit{max}}$ from $50$ to $450$ in steps of $25$.
• Figure 5: Zoom into high-$\overline{l}$ range of Fig. \ref{['fig:complexitySKF']} with the SKFs re-expressed in terms of the gains relative to the SDA result for $l_{\textit{max}}=500$ from Fig.s \ref{['fig:range']} and \ref{['fig:plotEx1']}.