Information reconciliation plays a crucial role in continuous-variable quantum key distribution (CVQKD), directly affecting the secret key rate and the maximum secure transmission distance. As the demand for CVQKD in both long-distance and numerous-user access network scenarios increases, high-performance error-correction codes tailored for low-SNR environments become essential for efficient reconciliation. However, traditional approaches face challenges such as complex construction and high system overhead, which hinder further development. To address these issues, we propose an error-correction scheme for CVQKD based on low-density parity-check (LDPC)-Hadamard codes, which incorporates multidimensional reconciliation and greatly simplifies the construction of low-rate codes, enabling efficient error correction at a code rate on the order of 0.001 without requiring multiple interactions. Results show that the LDPC-Hadamard-based reconciliation protocol achieves a code rate as low as 0.001 with a reconciliation efficiency of 95.98% at a signal-to-noise ratio of $-28.40$ dB, pushing the error-correction code rate formally into the thousandths regime while maintaining code lengths in the megabit range. The proposed method provides a practical technological foundation for point-to-point long-distance QKD and large-scale downstream CVQKD networks that support numerous users.

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• Information & communication theory
• Quantum communication, protocols & technology
• Quantum cryptography
• Quantum error correction
• Quantum information processing with continuous variables
• Quantum information theory
• Quantum networks