Check-ratio-aided Layer-based Rescaling ANMSA and Its Application for 5G-NR LDPC Codes.

As a kind of iterative decoding algorithms based on belief propagation (BP), sum-product algorithm (SPA) is capacity-approaching but scale-variant. Currently, however, excellent performance and great stability are still incompatible for min-sum algorithm (MSA) and its improvements. To remedy above problems, we firstly introduce the concept of rescaling, and disclose the causes of the performance loss of MSA. Then introduce the asymptotic optimal decoding algorithm, as well as the suboptimal one. Finally, a more practicable algorithm is proposed, called check-ratio-aided layer-based rescaling adaptive normalized MSA (CL-RANMSA). Compared with the first two algorithms, CL-RANMSA is both capacity-approaching and characteristically robust. In particular, the practicably optimal factors for base graph 2 in 5G new radio low-density parity check (5G-NR LDPC) codes are provided. Simulations are also carried out whose results depict its scale-invariance and excellent performance.