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International Conference on Information and Communication Technology Convergence (ICTC)

Error-Correction Method Based on LDPC for Quantum Key Distribution Systems

Bohdan Bilash, Byung Kwon Park, Chang-Hoon Park, Sang-Wook Han

Published Oct 21, 2020• 8 citations
Publisher

Abstract

We proposed an efficient error correction method for QKD systems using optimal LDPC check matrix. We divide sifted keys into 50 multiple parts, and each part creates syndrome using optimal check matrix. With this syndrome we have corrected the error of the sifted keys. By the proposed algorithm, we can correct less than 3 errors in each part of the sifted keys. The simulation results show that the error correction is performed efficiently.

DOI
10.1109/ictc49870.2020.9289451

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•Aug 23, 2021•2 citations
We proposed an efficient error correction method for QKD systems using optimal LDPC check matrix. We divide sifted keys into 50 multiple parts, and each part creates syndrome using optimal check matrix. With this syndrome we have corrected the error of the sifted keys. By the proposed algorithm, we can correct less than 3 errors in each part of the sifted keys. The simulation results show that the error correction is performed efficiently.
In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.
For the post-processing of the quantum-key-distribution (QKD) system, the error correction is the most important step, whose efficiency significantly influences the final key generation rate. Traditionally, the error-correction algorithm is developed based on the binary symmetrical channel model. However, this may not comply with the actual channel status. For example, for the fiber-based QKD system, differentiable statuses of the fiber (unstable or steady) should exist for some time and cause different bit error rates. If this channel feature can be exploited, it may considerably improve the error-correction efficiency. This paper proposes to introduce the Gilbert-Elliott (GE) model to analyze the QKD channel. The error-correction algorithm adopts the low-density parity-check (LDPC) code. The GE nodes are added into the traditional belief propagation (BP) algorithm of the LDPC decoder. Simulation results showed that the remaining frame error rate could be improved from ${10}^{\ensuremath{-}2}$ (or ${10}^{\ensuremath{-}3}$) to ${10}^{\ensuremath{-}4}$. An actual QKD system with the quantum channel state under manual control was adopted to collect the key bit string. By analyzing the occurrence probability of the kkk consecutive "1," the key bit string showed closely matched distribution with the GE model prediction. After the error correction, the remaining bit error rate of the modified BP algorithm was significantly smaller than that of the standard BP algorithm with an improvement of more than 2 orders of magnitude. Both simulation and actual experimental results demonstrate that our proposed method can greatly improve the error-correction efficiency if the channel characteristic of the QKD system is accurately exploited, which provides an efficient way to generate a higher key rate.
Quantum key distribution (QKD) is a promising technique to share unconditionally secure keys between remote parties. As an essential part of a practical QKD system, reconciliation is responsible for correcting the errors due to the quantum channel noise by exchanging information through a public classical channel. In the present work, we propose a novel syndrome-based low-density parity-check (LDPC) reconciliation protocol to reduce the information leakage of reconciliation by fully utilizing the syndrome information that was previously wasted. Both theoretical analysis and simulation results show that our protocol can evidently reduce the information leakage as well as the number of communication rounds.
This paper analyzes and adapts the known method of error correction of CV-QKD systems, proposed by Mario Milicevic, which modulates a code word with a correlated Gaussian sequence in amplitude and phase quadratures of coherent states, for use in DV-QKD systems, in which information is encoded by single-photon polarization states, by using a sieved key in the form of classical bits, from which the codeword is created, and also a one-time pad (Vernam cipher), which uses a fairly easy to implement classic Boolean “exclusive OR” operation (XOR). The main task of error correction is to correct errors in order to share the same secure key between the two parties (usually called Alice and Bob). Various factors can cause errors. The unreliability of the quantum channel is due to the fact that photons can cause noise when changing the polarization vector of the photon. In the proposed solution, the quantum component of the protocol occurs only in the first stage of transmission of the protected key, where the exchange of photons. The quantum key distribution system has inevitable errors in the sieved key, which must be corrected by the error correction algorithm to create a secure key. Unlike other known QKD systems, where at the stage of error correction the sifted keys are corrected and passed to the next stage of increasing confidentiality, in the modified method it is proposed to use sifted keys as keys in disposable Vernam ciphers, and the vector that will go to the next stage way and combine with the sifted key. The difference in the sieved keys between the two parties is corrected by means of low-density parity check matrices (LDPC), which are known to both of them in advance. Parity check matrices are created by an algorithm proposed by David MacKay and Radford Neal. Radford Neal open-source program code, is used to create final work program to checking proposed algorithm.
Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.