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A modified gradient descent bit-flipping (GDBF) algorithm is proposed for decoding low-density parity-check (LDPC) codes over the symmetric alpha-stable (SaS) impulsive noise channel. To simplify the log-likelihood rate (LLR) computational implement, this paper introduces a linear approximation of the LLR for the SaS impulsive noise. Combined with the linear approximation, the new algorithm introduces a penalty factor into the syndrome components of the inversion function. Simulation results show that the GDBF algorithm based on the penalty factor performs better than GDBF algorithm.