Quantum key distribution (QKD) relies on information reconciliation to determine transmission distance and secure key rate. Existing schemes (e.g., Cascade) demand costly multiround interaction, while binary LDPC-based methods suffer limited error correction capability. This work proposes a QKD reconciliation scheme using non-binary (NB) LDPC codes, combined with a rate-adaptive technique tailored to NB LDPC characteristics. Simulations show NB LDPC codes outperform binary counterparts in error correction performance and reconciliation efficiency-with gains increasing with finite field order, achieving 1.0661 over the finite field GF(128). The rate-adaptive technique extends fixed-rate code applicability, alleviating practical code construction and storage challenges.
Quantum key distribution (QKD) relies on information reconciliation to determine transmission distance and secure key rate. Existing schemes (e.g., Cascade) demand costly multiround interaction, while binary LDPC-based methods suffer limited error correction capability. This work proposes a QKD reconciliation scheme using non-binary (NB) LDPC codes, combined with a rate-adaptive technique tailored to NB LDPC characteristics. Simulations show NB LDPC codes outperform binary counterparts in error correction performance and reconciliation efficiency-with gains increasing with finite field order, achieving 1.0661 over the finite field GF(128). The rate-adaptive technique extends fixed-rate code applicability, alleviating practical code construction and storage challenges.
Abstract Non‐binary (NB) low‐density parity‐check (LDPC) codes over high‐order finite fields offer error‐correction performance closer to the Shannon limit while directly processing NB symbols, making them well‐suited for continuous‐variable quantum key distribution (CV‐QKD), which inherently involves high‐dimensional data. However, current CV‐QKD implementations have not been deeply researched in this area and still rely on binary error‐correcting codes, limiting the full exploitation of continuous‐variable information. Furthermore, the high sensitivity of CV‐QKD to signal‐to‐noise ratio (SNR) fluctuations renders fixed‐rate codes inadequate for practical channel variations. To address these issues, in this work an information reconciliation protocol is proposed based on rate‐adaptive NB LDPC codes. It not only leverages the advantages of using LDPC codes over NB fields, but also exploits their ability to directly correct NB symbols by incorporating rate‐adaptive techniques at both the symbol‐wise and bit‐wise granularity. Simulation results indicate that under identical conditions, reconciliation efficiency increases with field order, reaching 98.90% over Galois Field(GF)(64). In addition, both symbol‐wise and bit‐wise rate‐adaptive techniques extend the applicability of fixed‐rate NB LDPC codes, with the bit‐wise scheme consistently yielding higher secure‐key rates across all fields. Together, these techniques significantly enhance the efficiency and adaptability of CV‐QKD information reconciliation.
We study the information reconciliation (IR) scheme for quantum key distribution (QKD) protocols. The IR for the QKD can be seen as the asymmetric Slepian-Wolf problem, which low-density parity-check (LDPC) codes can solve with efficient algorithms, i.e., the belief propagation. However, the LDPC codes are needed to be chosen properly from a collection of codes optimized for multiple key rates, which leads to complex decoder devices and performance degradation for unoptimized key rates. Therefore, it is desired that establish an IR scheme with a single LDPC code which supports multiple rates. To this end, in this paper, we propose an IR scheme with a rate-compatible non-binary LDPC code. Numerical results show the proposed scheme achieves IR efficiency comparable to the best know conventional IR scheme with lower decoding error rates.
We develop a new approach for asymmetric LDPC-based information reconciliation in order to adapt to the current channel state and achieve better performance and scalability in practical resource-constrained QKD systems. The new scheme combines the advantages of LDPC codes, a priori error rate estimation, rate-adaptive and blind information reconciliation techniques. We compare the performance of several asymmetric and symmetric error correction schemes using a real industrial QKD setup. The proposed asymmetric algorithm achieves significantly higher throughput, providing a secret key rate that is close to the symmetric one in a wide range of error rates. Thus, our approach is found to be particularly efficient for applications with high key rates, limited classical channel capacity and asymmetric computational resource allocation.
Abstract In Quantum Key Distribution (QKD), two users extract a shared secret key using a quantum communication channel in the presence of an eavesdropper. Among QKD protocols, the ones based on Energy-Time (ET) entanglement of photons have been studied extensively due to their ability to generate high key rates from the arrival times of entangled photons. For the information reconciliation (IR) stage of ET-QKD protocols (where the users communicate using a classical channel in order to reconcile differences in their data), a scheme called multi-level coding (MLC) was proposed by Zhou et al. in prior work. The MLC scheme splits the raw key symbols into bit layers and utilizes binary Low-Density Parity-Check (LDPC) codes to encode each layer. Although binary LDPC codes are able to offer low complexity decoding for IR, they have poor error-correcting performance compared to their non-binary counterparts, thus leading to low key rates. Additionally, existing LDPC codes do not fully utilize the properties of the QKD channel to optimize the key rates. In this paper, we mitigate the above issues by proposing a flexible protocol for IR in ET-QKD systems called Non-Binary Multi-Level Coding NB-MLC(a) which is parameterized by a positive integer a. The NB-MLC(a) protocol is a generalization of the MLC scheme and utilizes NB-LDPC codes from a Galois field of size 2^a. We show that by using a small value of a, the NB-MLC(a) protocol significantly improves the key rate without much increase in complexity. To further improve the key rates of the NB-MLC(a) protocol, we propose i) a joint rate and degree distribution optimization (JRDO) algorithm to design the NB-LDPC codes for the protocol; ii) an interleaved decoding and communication (IDC) scheme to decode the different layers of the NB-MLC(a) protocol. The JRDO algorithm is designed to use the QKD channel information and we show that it results in a higher key rate than codes used in prior work. Additionally, the IDC scheme improves the key rate compared to the decoding and communication methods utilized previously in literature. Overall, the NB-MLC(a) protocol that uses JRDO LDPC codes and the IDC scheme results in a significant 40 − 60% improvement in key rates compared to prior work for ET-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.
Quantum Key Distribution (QKD) has been regarded as a novel approach to establish a secure communication between two legitimate partners. With the recent success of space based experimental QKD systems, researchers are now focussing on implementing more practical and efficient QKD systems that meet the challenges faced in space-based implementations. One pressing problem is the need for efficient and easy to implement reconciliation schemes for practical QKD systems. Rate-adaptive schemes based on LDPC codes constitute an appealing implementation of the key reconciliation process since they cover the entire range of the channel parameter space with a limited set of pre-defined Mother codes. In this paper, we investigate in detail some rate- adaptive reconciliation schemes based on LDPC codes, illustrating how their performance compares to other set-ups in which fixed-rate non- adaptive LDPC codes optimised for different channel conditions are adopted. In particular, the impact rate-adaptive codes have on decoding complexity, and subsequently the overall secure key throughput, is quantified through full blown simulations of an entanglement-based version of the QKD protocol within the context of an entanglement source onboard a satellite. Our work highlights that even though rate adaptive schemes schemes for QKD reconciliation appear ideal for future space-based implementations of single- photon QKD, identification of ideal Mother codes for such schemes remains to be resolved.