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arXiv:1505.06423

Simple rate-adaptive LDPC coding for quantum key distribution

Li, Mo, Chun-Mei Zhang, Zhen−Qiang Yin, Wei Chen, Chuan Wang, Zheng‐Fu Han

Published May 24, 2015• 2 citations
arXivHTMLPDF

Abstract

Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an easily implemented but efficiently rate-adaptive LDPC coding approach of reconciliation, different from the previously proposed puncturing- and shortening-based approach. We also give a measure for choosing the optimal LDPC parameter for our rate-adaptive approach according to error rates.

DOI
10.48550/arxiv.1505.06423

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Although quantum key distribution (QKD) comes from the development of quantum theory, the implementation of a practical QKD system does involve a lot of classical process, such as key reconciliation and privacy amplification, which is called post-processing. Post-processing has been a crucial element to high speed QKD systems, even the bottleneck of it because of its relatively high time consumption. Low density parity check (LDPC) is now becoming a promising approach of overcoming the bottleneck due to its good performance in processing throughput. In this article we propose and simulate an easily implemented but efficiently rate-adaptive LDPC coding approach of reconciliation, different from the previously proposed puncturing- and shortening-based approach. We also give a measure for choosing the optimal LDPC parameter for our rate-adaptive approach according to error rates.
The purpose of reconciliation, one of classical aspects of quantum key distribution (QKD) protocol, is to mitigate errors after the distribution of quantum information over a quantum channel. In this paper, a rate-adaptive method is proposed by means of a channel coding scheme where specific low-density parity-check (LDPC) codes are adapted in the Slepian-Wolf coding system. Puncturing and shortening techniques are adopted to optimize their coding rates with all possible cases of error in QKD. This successful method utilizes the knowledge of the quantum bit error rate (QBER) based on the maximum-likelihood estimator with respect to the syndrome information. Its benefit is that avoids wasting sample keys in the traditional channel estimation and thus increases the size of the final secret key. Evidently, simulation results confirm an improvement in the reconciliation efficiency with minimal interaction that suitable for high QKD throughput applications.
The postprocessing or secret-key distillation process in quantum key distribution (QKD) mainly involves two well-known procedures: information reconciliation and privacy amplification. Information or key reconciliation has been customarily studied in terms of efficiency. During this, some information needs to be disclosed for reconciling discrepancies in the exchanged keys. The leakage of information is lower bounded by a theoretical limit, and is usually parameterized by the reconciliation efficiency (or inefficiency), i.e. the ratio of additional information disclosed over the Shannon limit. Most techniques for reconciling errors in QKD try to optimize this parameter. For instance, the well-known Cascade (probably the most widely used procedure for reconciling errors in QKD) was recently shown to have an average efficiency of 1.05 at the cost of a high interactivity (number of exchanged messages). Modern coding techniques, such as rate-adaptive low-density parity-check (LDPC) codes were also shown to achieve similar efficiency values exchanging only one message, or even better values with few interactivity and shorter block-length codes.
In continuous-variable (CV) quantum key distribution (QKD), the reconciliation efficiency and frame error rate of the information reconciliation have a significant impact on the secret key rate. For a fixed-rate multiedge-type low-density parity-check (LDPC) code, the reconciliation efficiency and frame error rate will inevitably vary due to the fluctuations of the signal-to-noise ratio (SNR) of the CV QKD system, which degrades the performance of the system. We propose a high-efficiency rate-adaptive information reconciliation scheme by combining raptorlike (RL) LDPC codes with the addition of trusted noises. We establish the model of adding trusted noises and combine it with the RL LDPC codes to optimize the secret key rate under the time-varying channel. The simulation results show that our scheme can maintain a high reconciliation efficiency of more than 94.4% and a low frame error rate within 15% fluctuation range of the SNR. Furthermore, we implement the hardware acceleration of the proposed rate-adaptive scheme on a graphics processing unit and achieve a decoding throughput of 65.5 Mbits/s by optimizing the storage of the parity-check matrix. Our results are useful for the practical CV QKD under the realistic time-varying channel.
For high-speed quantum key distribution (QKD) post processing, information reconciliation is the most computational step, which usually acts as the system speed bottleneck. Reconciliation efficiency and operation throughput are the two most important performance parameters, but they are often compromised to each other in actual realization due to the available hardware resources. Another characteristic of the information reconciliation is that its channel is time-varying, and in order to guarantee high efficiency, some rate-compatible error correction scheme should be adopted. To cope with the above problems, this paper proposes a rate-compatible high-efficiency reconciliation algorithm based on quasi-cyclic (QC) low-density parity-check (LDPC) codes and puncturing algorithms. On the other hand, in order to obtain high throughput while maintaining low implementation complexity, the normalized min-sum algorithm (NMSA) is realized and optimized by using the fast prototyping tool of high-level synthesis (HLS). The proposed information reconciliation module was implemented on the Xilinx Zynq Ultrascale+ ZCU102 development board. Experimental results show that the maximum throughput rate of the implemented reconciliation module in this paper can reach 136 Mbps, while the efficiency factor is kept lower than 1.32 across the error rate range of 1.7%∼10.6% under the remaining frame error rate level of 10−3. The comprehensive good performance obtained by our design can strongly support the development of modern high-speed QKD systems.
In this paper, a rate-adaptive method is proposed an alternative reconciliation protocol by employing the LDPC-accumulate codes to the practical implementation in the quantum key distribution (QKD). The proposed rate-adaptive reconciliation is adapted in the Slepian-Wolf scheme where specific low-density parity-check (LDPC) codes are constructed by accumulated syndrome encoding/decoding. Its objective is to skip the step of quantum bit error rate (QBER) estimation by the traditional key sampling that increases the final secret key length in practice. From the numerical results, the proposed method achieves a good performance in terms of the number of disclosed bits and reconciliation efficiency comparable to the conventional Winnow, Cascade, and fixed-rate compatible LDPC based protocols. Moreover, it can cover the possible cases of error rates in the QKD system. Therefore, method is suitable for the highspeed discrete-variable QKD applications.
Information reconciliation is a crucial procedure in the classical post-processing of quantum key distribution (QKD). Poor reconciliation efficiency, revealing more information than strictly needed, may compromise the maximum attainable distance, while poor performance of the algorithm limits the practical throughput in a QKD device. Historically, reconciliation has been mainly done using close to minimal information disclosure but heavily interactive procedures, like \textit{Cascade}, or using less efficient but also less interactive ---just one message is exchanged--- procedures, like the ones based in low-density parity-check (LDPC) codes. The price to pay in the LDPC case is that good efficiency is only attained for very long codes and in a very narrow range centered around the quantum bit error rate (QBER) that the code was designed to reconcile, thus forcing to have several codes if a broad range of QBER needs to be catered for. Real world implementations of these methods are thus very demanding, either on computational or communication resources or both, to the extent that the last generation of GHz clocked QKD systems are finding a bottleneck in the classical part. In order to produce compact, high performance and reliable QKD systems it would be highly desirable to remove these problems. Here we analyse the use of short-length LDPC codes in the information reconciliation context using a low interactivity, \textit{blind}, protocol that avoids an a priori error rate estimation. We demonstrate that 2×1032 \times 10^32×103 bits length LDPC codes are suitable for blind reconciliation. Such codes are of high interest in practice, since they can be used for hardware implementations with very high throughput.