Abstract The error performance of the 5G low‐density parity‐check codes is significantly impacted by the update order of layers. At present, the row degree (RD) and the number of punctured bits (PBs) are widely used to decide the update order of layers. Here, the authors propose a metric to assess the soft message recovery speed of coded bits and then suggest updating layers with the lowest RD first rather than those with the least PBs first. Besides, a new criterion is introduced to further determine the update order of layers with the same number of PBs and the same RD. The resulting reordered layered schedule yields better error performance and faster convergence speed than the prior arts.
Abstract The error performance of the 5G low‐density parity‐check codes is significantly impacted by the update order of layers. At present, the row degree (RD) and the number of punctured bits (PBs) are widely used to decide the update order of layers. Here, the authors propose a metric to assess the soft message recovery speed of coded bits and then suggest updating layers with the lowest RD first rather than those with the least PBs first. Besides, a new criterion is introduced to further determine the update order of layers with the same number of PBs and the same RD. The resulting reordered layered schedule yields better error performance and faster convergence speed than the prior arts.
Low-density parity-check (LDPC) codes have been selected as the channel coding scheme for 5G NR standard, which have excellent performance approaching the Shannon limit and are easy to implement in hardware. The decoding algorithm and scheduling scheme of LDPC codes have a significant impact on performance. The row degree (RD) and the number of punctured bits (PBs) are widely used to determine the update order of layers. In this letter, we used Matlab to simulate the error performance of the 5G LDPC codes. We completed the bit error rate and frame error rate simulations of six different decoding algorithms, including flooding LLR-BP, flooding NMS, layered LLR-BP, layered NMS, the lowest degree and least-punctured (LD-LP) layered LLR-BP and LD-LP layered NMS methods, for the 5G LDPC code with a base graph of size [46, 68], code rate 1/3, and code length of 1584.We further compared the performance of LD-LP layered decoding and LP-LD layered decoding. Moreover, we simulated the error performance of the core part of the LDPC code, which consists of four layers. We evaluated the effect of the update order of the four layers on the error performance of the code, and concluded that some update orders might give slightly better error performance than others.
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.
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.
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 (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.