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IEEE Globecom Workshops (GC Wkshps)

Analysis of Efficient Scheduling in Layered Decoding of LDPC Codes

Dongxu Chang, Guanghui Wang, Guiying Yan, Zhi-Ming Ma

Published Dec 8, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1109/gcwkshp64532.2024.11100402

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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.
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.
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.
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 investigate the characteristics of scheduling sequences that enable efficient decoding of generalized low-density parity-check (GLDPC) codes under the layered message-passing algorithm. In particular, we show that scheduling sequences leading to higher decoding efficiency should prioritize the update of constraint nodes corresponding to subcodes with larger minimum distance, fewer minimum-weight codewords, and shorter code length. Based on these characteristics, we design a scheduling algorithm, which further demonstrates the effectiveness of these characteristics through simulation experiments.
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.