Very-low-complexity decoding algorithm for low-density parity-check codes

In this paper, we propose a new very-low-complexity (VLC) decoding algorithm for low-density parity-check (LDPC) codes. This new algorithm only need subtract a correcting factor to improve the accuracy of the soft message values delivered by a previously proposed simplified belief-propagation (BP)-based algorithm called uniformly most powerful (UMP) algorithm. However, the VLC algorithm outperforms the UMP algorithm greatly. The correcting factor can be obtained by simulation or theoretical derivation. This new VLC algorithm is much simpler to implement than BP algorithm, and also simpler than previously proposed normalized BP-based algorithm in which the operation of dividing a normalization factor is needed. However, the performance of the VLC algorithm is slightly better than that of the normalized BP-based algorithm. Also, the VLC algorithm is universal in that the decoding is independent of the channel characteristics. Simulation results demonstrate that the performance of the new VLC algorithm can nearly approach that of BP on the additive white Gaussian noise (AWGN) channel.