An Analysis and Design of Rate-dependent Nested Scheduling in Layered Decoding of LDPC Codes

In this study, we analyze the characteristics of scheduling sequences for layered belief propagation (LBP) that can result in efficient decoding of low-density parity-check (LDPC) codes. Specifically, we claim that scheduling sequences leading to high decoding efficiency should prioritize updating check nodes with lower error probabilities aggregated from neighboring variable nodes. We prove this conclusion separately on both the BEC and the BI-AWGN channels. Some observable characteristics in “good” scheduling sequences regarding row weights, rows connected to punctured columns, and column weights can serve as corollaries to this conclusion. By comprehensively considering these characteristics of good scheduling, we design a multi-sequence nested scheduling scheme of layered decoding for 5G New Radio (NR) LDPC codes. The proposed schemes can obtain scheduling sequences for various rates of rate-compatible LDPC codes using small hardware storage. What’s more, by respectively storing double-sequence, triple-sequence, or more sequences to obtain scheduling sequences at various code rates, a trade-off can be made between decoder storage and decoding performance. Experimental results demonstrate that the proposed scheme achieves performance improvements compared to existing scheduling schemes at nearly all code rates.