Modified Noisy Gradient Descent Bit-Flipping Decoding Algorithms for LDPC Codes

In this paper, we propose modified multi-bit noisy gradient descent bit flipping (M-NGDBF) algorithms for decoding low-density parity-check codes. To simplify the decoder design, we eliminate the use of Gaussian noise generators at the decoder and replace them with received signals after simple transformations. We then improve the convergence rate by removing the randomness in the M-NGDBF algorithm during the first few iterations. Subsequently, we construct a tabu-list to record bits that are flipped in the current iteration and allows these bits to be flipped in the next iteration only with a very small probability. Simulation results show that our proposed algorithms outperform the original M-NGDBF algorithm in terms of both bit error rate and convergence rate.