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IEEE Communications Letters

Two Effective Scheduling Schemes for Layered Belief Propagation of 5G LDPC Codes

Bingbing Wang, Yan Zhu, Jing Kang

Published Apr 30, 2020• 40 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2020.2991473

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IEEE Transactions on Communications•Jul 3, 2025•2 citations
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.
Quasi-cyclic low-density parity-check codes (QC-LDPC) are selected as the channel coding scheme for the data channel of the new radio (NR) enhanced mobile broadband (eMBB) in fifth-generation (5G) mobile communication technology. Traditional layered scheduling strategies used in 5G LDPC codes improve decoding convergence speed, but fixed scheduling schemes cannot fully utilize dynamic changes in decoded messages. To address this issue, this paper proposes a layered scheduling scheme for 5G LDPC codes based on edge information. By prioritizing updates to layers with minimal changes in edge information, this method reduces decoding complexity and accelerates convergence with minimal performance loss. Simulation results demonstrate that this approach enhances decoding performance by approximately 0.05dB compared to other improved hierarchical scheduling strategies.
In this paper, we propose two new scheduling algorithms to address the issues of existing informed dynamic scheduling (IDS) decoding algorithms of short low-density parity-check (LDPC) codes for the fifth-generation (5G) new radio (NR). The first issue is the complexity problem, where the high complexity of IDS makes hardware implementation difficult. By considering the impact of puncturing for the first two columns of base matrices, the proposed least-punctured and sum-residual-based (LPSRB) algorithm can reduce decoding complexity. The second issue is the significant degradation of decoding performance when the code length is short. By fully utilizing residuals, the proposed novel residual belief propagation (NRBP) algorithm allocates a significant amount of decoding resources to the less convergent edges. Simulation results demonstrate that NRBP achieves better frame error rate (FER) performance for short LDPC codes.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
We present an enhanced informed dynamic scheduling (IDS) strategy to avoid propagations of unreliable messages in the residual belief-propagation (RBP) algorithm for decoding low-density parity-check (LDPC) codes. To reduce the resource needed for updating the degree-one variable nodes (VNs) in an RBP-based algorithm for decoding 5G New Radio (NR) LDPC codes, we further introduce a process consisting of several simple procedures for managing the resource consumption. Simulation results demonstrate that our RBP algorithm based on the proposed IDS strategy outperforms existing RBP-based algorithms at the early decoding iterations. By using our degree-one VN resource managing approach, the performance of both the proposed and the existing decoders is significantly improved in decoding the 5G NR codes.
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.
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.