In satellite-ground quantum key distribution, two legitimate users, Alice and Bob, complete the key distribution by satellite-ground link window. After key distribution, Alice and Bob have inconsistent key sequences X and Y. The two sides transmit part of the information sequence through the ideal public authorized channel, and consistent key sequences are obtained, which is called key error correction in data reconciliation. In key error correction, information sequence transmitted by the ideal public authorized channel is the check sequence generated by X. Encode module of key sequence is required to occupy less FPGA resources, and the encoding speed is fast. A coding scheme based on FPGA and turbo codes is proposed. It takes less FPGA resources, fast coding speed and can select the coding bit rate according to the demands.