Modified Gradient Descent Bit-Flipping Decoding for Low-Density Parity-Check Codes

Abstract

In this paper, we modify the gradient descent bit-flipping (GDBF) decoding of low-density parity-check codes based on the syndrome. Firstly, the syndrome weight is utilized to detect the decoding loop, which seriously effects the performance of GDBF decoding. Then the syndrome information is introduced to update the reliability of the flipped bit nodes. Since the modified GDBF, denoted as MGDBF, only uses the syndrome weight and syndrome information, there is small complexity increased. Simulation results indicate that the two modifications bring about significant improvement in error-rate performance. For single MGDBF decoding, its performance is not only better than that of GDBF, but also is better than that of noisy GDBF. For multi MGDBF decoding, it can obtain fast convergence rate and good performance by employing the appropriate adaptive threshold scheme.