Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems

Jeongseok Ha,Hyunwoo Jung,Suhwang Jeong

doi:10.1038/s41534-021-00509-9

Abstract

In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.

Highlights

Quantum key distribution (QKD) systems allow two remote parties to share secret keys by utilizing quantum mechanics[1], which is known to provide unconditional security[2,3]
QKD systems are usually categorized into discrete-variable QKD (DV-QKD)[1,2,4], and continuous-variable QKD (CV-QKD) systems[5,6,7], according to their modulation techniques adopted in the quantum state exchanges
In the DV-QKD systems, the polarization of the single-photon is modulated by the information while both the amplitude and phase quadrature of coherent state are modulated in the CV-QKD systems

Summary

INTRODUCTION

Quantum key distribution (QKD) systems allow two remote parties to share secret keys by utilizing quantum mechanics[1], which is known to provide unconditional security[2,3]. 0~ 1⁄4 ðo[1]; o2; 1⁄4 ; one Þ is a vector of length ne, om 1⁄4 t m 2 E2 and zeros for the other elements It is shown in Theorem 1 that an MET-LDPC code ensemble with degree-one variable nodes has exponentially few codewords of small weights when the infimum of the solution set for the equation in Eq (5) is larger than one, which is the t-value condition and summarized in Definition 2. We will show that it is possible to design rate-compatible METLDPC codes with good error-rate performances in both the threshold and error-floor regions, which is carried out by proving that there exists a sequence of punctured MET-LDPC code ensembles of rates with exponentially few codewords of small weights To this end, we utilize the design rule in ref. Instead of the key rate in Eq (16), as suggested in ref. 16, we use a

C2 19 C1π C2π

DISCUSSION

CODE AVAILABILITY