An escape method for the local optima of the gradient descent bit-flipping (GDBF) algorithm for decoding low-density parity-check codes is proposed. In the GDBF algorithm, a search point is likely to be trapped in a local optimum, which causes performance degradation of the algorithm. To address this issue, we introduce a list to store the frequency of visits to each local optimum and devise a strategy to increase the distance of a search point from a local optimum with respect to the frequency. (c) 2015 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.