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arXiv:2506.13507

Dynamic Layered Decoding Scheduling for LDPC Codes Aided by Check Node Unsatisfied Probabilities

Chenyuan Jia, Chang, Dongxu, Wang, Ruiyuan, Guanghui Wang, Guiying Yan, Cunquan Qu

Published Jun 16, 2025• 0 citations
arXivHTMLPDF

Abstract

This letter revisits update ordering in layered belief propagation (LBP) decoding of low-density parity-check (LDPC) codes. The closest probability-based schedule orders layers by check node unsatisfied probabilities estimated only from the channel observations, although these probabilities change once decoding messages are exchanged. We therefore refresh the check node unsatisfied probabilities during decoding and use them as dynamic priorities. The first schedule, Dyn-EBP, selects the most reliable available check node while ensuring that every check node is updated once in each iteration. The second schedule, Dyn-PEBP, adds a linear update-count penalty and allows limited repeated updates without letting a small subset of check nodes dominate the schedule. For 5G new radio LDPC base graph 1 codes with five iterations, the proposed schedules yield small BLER reductions relative to the channel-only probability schedule and remain competitive with LBP, LPHD scheduling, and RD-RBP. The gain is modest, but it shows that probability-based scheduling benefits from message-level refinement.

DOI
10.48550/arxiv.2506.13507

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This letter revisits update ordering in layered belief propagation (LBP) decoding of low-density parity-check (LDPC) codes. The closest probability-based schedule orders layers by check node unsatisfied probabilities estimated only from the channel observations, although these probabilities change once decoding messages are exchanged. We therefore refresh the check node unsatisfied probabilities during decoding and use them as dynamic priorities. The first schedule, Dyn-EBP, selects the most reliable available check node while ensuring that every check node is updated once in each iteration. The second schedule, Dyn-PEBP, adds a linear update-count penalty and allows limited repeated updates without letting a small subset of check nodes dominate the schedule. For 5G new radio LDPC base graph 1 codes with five iterations, the proposed schedules yield small BLER reductions relative to the channel-only probability schedule and remain competitive with LBP, LPHD scheduling, and RD-RBP. The gain is modest, but it shows that probability-based scheduling benefits from message-level refinement.
Low-density parity-check (LDPC) codes have been chosen for the fifth-generation (5G) new radio (NR) enhanced Mobile Broad Band (eMBB) data channel. Since NR LDPC codes puncture the first two block columns of the parity-check matrix, the decoding complexity is reduced, but it slows down the convergence rate. In this letter, we propose a fixed schedule that decodes the layers with the least-punctured edges and those with the highest-degree (LPHD), which has much faster convergence speed than conventional schemes. The fixed scheduling schemes cannot take full advantage of the dynamic changes of decoding messages. As a result, the residual-based layered belief propagation (RB-LBP) is proposed to rearrange the layers dynamically among different iterations. Compared with some informed dynamic scheduling (IDS) strategies, RB-LBP reduces the decoding complexity with slight performance loss.
Schedule plays an important role in layered belief propagation (BP) decoding of low-density parity-check (LDPC) codes. It affects the error-rate performance as well as convergence rate of the decoder. In this paper, an efficient scheduling scheme is proposed to arrange the updating order of check nodes for layered BP decoder of regular LDPC codes. This scheme selects check node one at a time based on the reliability of the variable nodes. Specifically each time the check node with maximum number of low-reliability neighbors is selected. For simplicity, we introduce the updating state instead of the real-time messages to represent variable-node reliability. Simulation results on regular LDPC codes prove that the proposed scheduling scheme can obtain efficient schedules with fast convergence and good error-rate performance.
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.
Compared to classic channel coding,Low-density parity-check(LDPC) codes have proved to be very powerful channel coding schemes with a broad range of applications.However,as maximum-likelihood decoding is too complex to implement,suboptimal decoders have to be employed.One of the most popular decoding algorithms of LDPC codes is belief propagation(BP) decoding.Informed Dynamic Scheduling(IDS) can provide a better BER performance,but hard to implement due to high computational complexity increased.In order to improve the convergence,a simple low-complexity sequential check-node-based scheduling strategy is proposed.A new check-node-based reliability measure is defined,which represents the degree of reliability approximately.The reliability measure is used for ordering while the actual message updates still use the exact BP equations.During an iteration,the schedule strategy finds an update sequence,which is arranged by the new defined reliability measure in ascending order.Complexity is compared among those algorithms.Mechanism why the new strategy works effective is presented.Simulation shows that the new approach significantly improves the BER performance using short-length block LDPC codes and reduces iterations.
In this study, we analyze the characteristics of scheduling sequences for Layered belief propagation (LBP) that can result in efficient decoding on 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 in both BEC and 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. Based on these, we design a dynamic scheduling algorithm, which can further demonstrate the effectiveness of these characteristics through simulation experiments.
Scheduling strategy is considered an important aspect of belief-propagation (BP) decoding of low-density parity-check (LDPC) codes because it affects the decoder's convergence rate, decoding complexity and error-correction performance. In this paper, we propose two new scheduling strategies for the BP decoding of non-binary LDPC (NB-LDPC) codes. Both the strategies are devised based on the concept of check node reliability and employ a heuristically defined threshold which can adapt to the communication channel variations. As the scheduling strategies only update a subset of the check nodes in each iteration, they result in reduced iteration cost. Furthermore, since the BP performs suboptimally for finite-length LDPC codes, especially for short-length LDPC codes, by enhancing the message propagation over the Tanner Graphs of short-length NB-LDPC codes, the new scheduling strategies can even improve the error-correction performances of BP decoding. Simulation results demonstrate that the new scheduling strategies provide good performance/complexity tradeoffs.