Information reconciliation (IR) corrects the errors in sifted keys and ensures the correctness of quantum key distribution (QKD) systems. Polar codes-based IR schemes can achieve high reconciliation efficiency, however, the incidental high frame error rate decreases the secure key rate of QKD systems. In this article, we propose a Shannon-limit approached (SLA) IR scheme, which mainly contains two phases: the forward reconciliation phase and the acknowledgment reconciliation phase. In the forward reconciliation phase, the sifted key is divided into sub-blocks and performed with the improved block checked successive cancellation list (BC-SCL) decoder of polar codes. Afterwards, only the failure corrected sub-blocks perform the additional acknowledgment reconciliation phase, which decreases the frame error rate of the SLA IR scheme. The experimental results show that the overall failure probability of SLA IR scheme is decreased to $10^{-8}$ and the efficiency is improved to 1.091 with the IR block length of 128Mb. Furthermore, the efficiency of the proposed SLA IR scheme is 1.055, approached to Shannon-limit, when quantum bit error rate is 0.02 and the input scale of 1Gb, which is hundred times larger than the state-of-art implemented polar codes-based IR schemes.
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