Rate‐Adaptive Non‐Binary LDPC Code‐Based Information Reconciliation Protocol for Continuous‐Variable Quantum Key Distribution

Abstract

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.