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Given the Tanner graph of a generalized low-density parity-check (GLDPC) code, the decoding complexity is mainly dominated by the decoding algorithm of subcodes. In this paper, we propose a class of GLDPC codes with fast parallel decoding algorithm. The parity-check matrices of the newly constructed subcodes are composed of several square matrices, which can be viewed as elements of a finite field. Therefore the FFT-based a posteriori probability (APP) algorithm for nonbinary codes can be applied to decode the subcodes. When compared with the trellis-based APP algorithm, the FFT-based APP algorithm can be implemented in parallel and has lower complexity. Simulation results show that the proposed GLDPC codes perform well on AWGN channels.