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IEEE Transactions on Vehicular Technology

Reduced Complexity Dynamic Schedule for Layered Decoding of LDPC Codes

Xinle Jia, Yangcan Zhou, Zijian Qin, Jingjing Zhu, Zhongfeng Wang

Published Mar 14, 2025• 3 citations
Publisher

Abstract

Low-density parity-check (LDPC) codes have been selected as the coding scheme of the data channel in 5G communication. To enhance the performance of conventional layered decoding of LDPC codes, various dynamic schedules have been proposed recently. However, these dynamic schedules suffer from high complexity. In this paper, we propose a reduced complexity dynamic layered schedule for LDPC codes, where the layer to be updated is determined based on the residual of each layer. Moreover, an adjustable parameter is introduced to achieve a better performance-complexity trade-off. Simulation results show that the proposed method maintains excellent error-correction performance while the computational complexity is greatly reduced, compared to the prior dynamic schedules.

DOI
10.1109/tvt.2025.3551240

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Low-density parity-check (LDPC) codes have been selected as the coding scheme of the data channel in 5G communication. To enhance the performance of conventional layered decoding of LDPC codes, various dynamic schedules have been proposed recently. However, these dynamic schedules suffer from high complexity. In this paper, we propose a reduced complexity dynamic layered schedule for LDPC codes, where the layer to be updated is determined based on the residual of each layer. Moreover, an adjustable parameter is introduced to achieve a better performance-complexity trade-off. Simulation results show that the proposed method maintains excellent error-correction performance while the computational complexity is greatly reduced, compared to the prior dynamic schedules.
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.
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.
Beside the well known iterative Belief Propagation algorithm several alternative decoding schemes for Low-Density Parity-Check (LDPC) codes providing better performance in terms of residual error rate, convergence speed or computational complexity have been developed in the last years. Recently, Informed Dynamic Scheduling has been proposed in [1] providing different decoding strategies that dynamically decide which messages are passed throughout the decoding process. It was shown that the overall convergence can be sped up considerably and also more errors can be corrected compared to other (non-dynamic) decoding strategies. However, these improvements are somehow overshadowed by a significant amount of additional computational complexity that is needed for the selection of the messages to be updated in each decoding step. We propose two novel dynamic decoding strategies that allow for a flexible adaptation of the decoder's dynamics and reduce the additional complexity remarkably while maintaining, and in some cases even exceeding, the convergence speed and error rate performance of currently known dynamic schedules.
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.
Quasi-cyclic low-density parity-check (QC-LDPC) codes have been selected as the channel coding scheme for 5G new radio (NR) data channel. In this letter, a novel base graph based static scheduling (BGSS) method is proposed for layered decoding of 5G LDPC codes to accelerate decoding convergence and reduce the average number of iterations (ANI). In the proposed BGSS method, the update order of layers is determined based on row weight, column weight and number of punctured non-zero elements of BG matrix. Three optimization rules are included in BGSS to determine the order: 1) The layer with less punctured non-zero element is updated firstly. 2) The layer with relatively small row weight is updated firstly. 3) The layer which can utilize more recent information is updated firstly. The first rule has the highest priority and the third rule has the lowest priority. Simulation results show that compared with other scheduling method, the proposed method reduces about 1.1 ANI and obtains about 0.05dB performance gain for given LDPC codes.
Low-density parity-check (LDPC) codes offer excellent performance at competitive levels of complexity. Short block length LDPC codes avoid the large processing latency incurred by the large block lengths classically considered for this class of codes, making them a potential candidate for next generation wireless communications systems. In this paper, a novel informed dynamic scheduling (IDS) approach for decoding LDPC codes is developed based on the use of the current message reliabilities and the residuals of the potential updates to select the messages passed in the graph during iterative Sum Product decoding. An alternative measure of the iteration of the IDS schemes is also proposed which highlights the high cost of those algorithms in terms of processing complexity and motivates the development of the proposed approach. The proposed Rel.-RBP decoding algorithm offers very fast convergence at reduced complexity and gains in error rate performance when compared to the previous schemes.