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Information Reconciliation for Continuous-Variable Quantum Key Distribution with $β> 1$ Using Short Blocklength Error Correction Codes: Proposal and Concerns

Kadir Gümüş, João dos Reis Frazão, Aaron Albores-Mejia, Boris Škorić, Gabriele Liga, Yunus Can Gültekin, Thomas Bradley, Chigo Okonkwo

TL;DR

The paper addresses reconciliation in continuous-variable QKD with the goal of achieving reconciliation efficiency $\beta>1$ using short-blocklength error-correction codes. It proposes a two-stage decoding protocol, combining a short, low-rate inner code with a long, high-rate outer code and a frame-acceptance mechanism based on a quality metric to increase the information extracted from accepted frames. Simulations using TBP-LDPC codes show potential gains in $\beta_t$ (up to around 1.4) and increased reliable key rates, while highlighting the trade-off with frame rejection and finite-size effects. The paper also discusses critical security concerns about frame rejection, leakage, and the need for rigorous security proofs before claims on SKR or distance can be made.

Abstract

In this paper, we introduce a reconciliation protocol with a two-step error correction scheme that uses a short-blocklength, low-rate code and a long-blocklength, high-rate code. We simulate the protocol using a short-block-length low-density parity-check code and show that we can achieve reconciliation efficiencies above 1 using this method. We discuss the necessary steps required regarding security proofs before this protocol can be securely implemented.

Information Reconciliation for Continuous-Variable Quantum Key Distribution with $β> 1$ Using Short Blocklength Error Correction Codes: Proposal and Concerns

TL;DR

The paper addresses reconciliation in continuous-variable QKD with the goal of achieving reconciliation efficiency using short-blocklength error-correction codes. It proposes a two-stage decoding protocol, combining a short, low-rate inner code with a long, high-rate outer code and a frame-acceptance mechanism based on a quality metric to increase the information extracted from accepted frames. Simulations using TBP-LDPC codes show potential gains in (up to around 1.4) and increased reliable key rates, while highlighting the trade-off with frame rejection and finite-size effects. The paper also discusses critical security concerns about frame rejection, leakage, and the need for rigorous security proofs before claims on SKR or distance can be made.

Abstract

In this paper, we introduce a reconciliation protocol with a two-step error correction scheme that uses a short-blocklength, low-rate code and a long-blocklength, high-rate code. We simulate the protocol using a short-block-length low-density parity-check code and show that we can achieve reconciliation efficiencies above 1 using this method. We discuss the necessary steps required regarding security proofs before this protocol can be securely implemented.
Paper Structure (6 sections, 4 equations, 7 figures)

This paper contains 6 sections, 4 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Multi-dimensional Reconciliation
  3. Proposed Reconciliation Protocol
  4. Results
  5. Security Considerations
  6. Conclusion

Figures (7)

  • Figure 1: An overview of multi-dimensional reconciliation.
  • Figure 2: An overview of our proposed reconciliation protocol based on multi-dimensional reconciliation.
  • Figure 3: An overview of the second error correction step using a high-rate code.
  • Figure 4: $\text{BER}_{AF}$ (---) and $1-h(\text{BER}_{AF})$ (------) vs. AFR for different $\beta_{in}$. The error correction code used is a $R_{in} = \frac{1}{50}$ TBP-LDPC code with $N_{in} = 500$.
  • Figure 5: $\beta_t$ vs. AFR for our proposed protocol for different $\beta_{in}$, assuming $\beta_{out} = 1$. The error correction code used is a $R_{in} = \frac{1}{50}$ TBP-LDPC code with $N_{in} = 500$.
  • ...and 2 more figures