Improved second minimum value for Probabilistic Min-Sum Algorithm in LDPC decoding

Abdelilah Kadi, Saïd Najah, Mostafa Mrabti +1 more

Huang–Chang Lee, Chung-Chao Cheng, Yeong-Luh Ueng

In order to simplify the check node operation of the low-density parity-check (LDPC) decoders, this paper presents a Normalized Probabilistic Min-Sum Algorithm (NPMSA), where the second minimum value is replaced by a probabilistic second minimum value. For NPMSA, the number of required comparisons can be reduced to about half compared to that of the conventional Normalized Min-Sum Algorithm (NMSA). It is shown that the simplification only introduces negligible impact on the bit-error rate performance, especially for codes with a high check node degree. When the proposed NPMSA is applied to the (2048, 1723) RS-LDPC code, the degradation in the error-rate performance is only about 0.05 dB. The hardware implementation shows that a throughput of 45.42 Gbps can be achieved using the proposed NPMSA.

Chenxuan Wang, Cheng-Hung Dixson Lin

The hardware design of the probabilistic min-sum algorithm can be efficiently realized by group searching. Although it can accelerate calculation and reduce hardware complexity, it degrades error correction capability. Thus, an improved method for simplified min-sum algorithm is proposed in this paper. In order to recover the error correction capability, we apply the accurate first minimum for adjusting the reliability of the probabilistic second minimum. Maintaining the value of the first minimum and proportionally combining the first two minima can flexibly improve the reliability of probabilistic second minimum. Compared with the original simplified min-sum algorithm, the improved method not only gains the efficient hardware design but also obtains the better error correction capability.

Juntan Zhang, M.P.C. Fossorier, Daqing Gu +1 more

Joan Marc Català Pérez, Jesus O. Lacruz, Francisco García-Herrero +2 more

Zijian Qin, Yangcan Zhou, Zhongfeng Wang

Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.