Information Reconciliation for QKD with Rate-Compatible Non-Binary LDPC Codes

Guo Limei, Ran Qi, Jin Di +1 more

Chao Zhou, Xiangyu Wang, Zhiguo Zhang +3 more

Kenta Kasai, Ryutaroh Matsumoto, Kohichi Sakaniwa

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.

Kun Zhang, Jia Hou, Xueqin Jiang +3 more

Qixiang Chen, Jiajia Han, Yuxiang Lv +4 more

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.

Debarnab Mitra, Jayanth Shreekumar, Lev Tauz +3 more

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.