  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.
