For the post-processing of the quantum-key-distribution (QKD) system, the error correction is the most important step, whose efficiency significantly influences the final key generation rate. Traditionally, the error-correction algorithm is developed based on the binary symmetrical channel model. However, this may not comply with the actual channel status. For example, for the fiber-based QKD system, differentiable statuses of the fiber (unstable or steady) should exist for some time and cause different bit error rates. If this channel feature can be exploited, it may considerably improve the error-correction efficiency. This paper proposes to introduce the Gilbert-Elliott (GE) model to analyze the QKD channel. The error-correction algorithm adopts the low-density parity-check (LDPC) code. The GE nodes are added into the traditional belief propagation (BP) algorithm of the LDPC decoder. Simulation results showed that the remaining frame error rate could be improved from ${10}^{-2}$ (or ${10}^{-3}$) to ${10}^{-4}$. An actual QKD system with the quantum channel state under manual control was adopted to collect the key bit string. By analyzing the occurrence probability of the $k$ consecutive "1," the key bit string showed closely matched distribution with the GE model prediction. After the error correction, the remaining bit error rate of the modified BP algorithm was significantly smaller than that of the standard BP algorithm with an improvement of more than 2 orders of magnitude. Both simulation and actual experimental results demonstrate that our proposed method can greatly improve the error-correction efficiency if the channel characteristic of the QKD system is accurately exploited, which provides an efficient way to generate a higher key rate.

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• Quantum communication
• Quantum parameter estimation