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IEEE Globecom Workshops (GC Wkshps)

Low-Complexity Layered Decoding for LDPC Codes

Heping Wan, Joonyoung Cho, Min Jang, Jianzhong Charlie Zhang

Published Dec 8, 2024• 0 citations
Publisher

Abstract

This paper presents methods to reduce the complexity of the layered decoding for LDPC codes with negligibly impacting the error-correcting performance. We accomplish this by deactivating variable nodes. The LLR updates associated with the deactivated variable nodes are skipped. To determine which variable nodes should be deactivated, the most reliable bit-level channels, derived from the M−ary input channel, are identified. Then, from the variable nodes assigned to the most reliable bit-level channels, we select those with initial LLRs above a threshold as the deactivated variable nodes. We establish an analytical relationship between the threshold and a desired error probability. The threshold can be adjusted accordingly by specifying the desired error probability. The standard 5G LDPC codes are simulated. By setting the desired error probability to 10−3, more than 20% of the variable nodes are deactivated while the error-correcting performance is preserved.

DOI
10.1109/gcwkshp64532.2024.11100976

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This paper presents methods to reduce the complexity of the layered decoding for LDPC codes with negligibly impacting the error-correcting performance. We accomplish this by deactivating variable nodes. The LLR updates associated with the deactivated variable nodes are skipped. To determine which variable nodes should be deactivated, the most reliable bit-level channels, derived from the M−ary input channel, are identified. Then, from the variable nodes assigned to the most reliable bit-level channels, we select those with initial LLRs above a threshold as the deactivated variable nodes. We establish an analytical relationship between the threshold and a desired error probability. The threshold can be adjusted accordingly by specifying the desired error probability. The standard 5G LDPC codes are simulated. By setting the desired error probability to 10−3, more than 20% of the variable nodes are deactivated while the error-correcting performance is preserved.
Two methods are proposed to reduce the complexity of the belief propagation (BP) decoding for low-density parity-check (LDPC) codes, with the focus on the layered decoding for quasi-cyclic LDPC (QC-LDPC) codes. The two methods can be separately incorporated into the layered decoding procedures and combined seamlessly to provide the two-fold complexity reduction. In the first method, the message updates regarding a subset of variable nodes are omitted. To construct the subset, the most reliable bit-level channels, derived fromM-ary input channels, are identified. Then, we select the variable nodes with initial log-likelihood ratios (LLRs) exceeding a threshold among the ones assigned to the most reliable bit-level channels to form the subset. The threshold is designed and adjusted based on characteristics of the most reliable bit-level channels. Our numerical results demonstrate that the first method significantly reduces the complexity with negligibly impacting the error-correcting performance. In the second method, each layer of base graphs of QC-LDPC codes uses either sum-product algorithm (SPA) or min-sum algorithm (MSA) to update LLRs. A degree-based algorithm is presented to determine the layers employing either SPA or MSA. We compare with two intuitive methods: 1) applying SPA to randomly selected layers and MSA to the remaining layers, and 2) applying SPA to the core layers of 5G NR LDPC codes and MSA to the remaining layers. According to the numerical results, the degree-based algorithm maximally reduces the complexity while maintaining the same performance. To evaluate the joint method, the first method is applied on top of the second method. Further complexity reduction is achieved without degrading the performance of the second method.
A modified message propagation algorithm is proposed for a low-complexity decoder of low-density parity-check (LDPC) codes, which controls the information propagated from variable and check nodes.The proposed threshold-based node deactivation for variable nodes and zero-forcing scheme for check nodes remarkably reduce decoding complexity required for similar error performance. In the proposed scheme, different thresholds, which are determined from the base matrix of the LDPC codes, are applied for each type of variable node. In addition, thresholds for deactivating variable nodes are increased while the decoding process is operated for a reduction in decoding complexity without early error floor, which is a drawback of the conventional threshold-based deactivation scheme. Simulation results show that the proposed scheme enables normalized min-sum decoders to decode successfully with less complexity than the conventional threshold-based deactivating scheme.
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 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.
In order to reduce the bit error rate of low-density parity-check codes for layered decoding algorithm and improve the decoding convergence speed, an improved layered decoding algorithm is proposed. In layered decoding algorithm, updated bit nodes information can be used by check nodes in the iteration process while in dynamic decoding algorithm check nodes update in order according to the reliability. The proposed algorithm combines advantages of the layered and dynamic decoding algorithm. Moreover, compared with the definition of remaining information for check nodes in the dynamic decoding algorithm, a new method to evaluate the reliability is defined in the proposed algorithm. Based on 1/2 code rate china mobile multimedia broadcasting standard, simulation and comparison between the conventional layered decoding algorithm and the proposed layered decoding algorithm have been carried out. The simulation results show that under the same bit error rate, the signal to noise ratio of the improved algorithm reduces nearly 0.4dB as well as convergence speed improves obviously. The proposed layered decoding algorithm reduces the bit error rate and improves the reliability of data in communication system which uses LDPC codes as the channel coding.
This paper presents novel techniques for improving the error correction performance and reducing the complexity of coarsely quantized 5G LDPC decoders. The proposed decoder design supports arbitrary message-passing schedules on a base-matrix level by modeling exchanged messages with entry-specific discrete random variables. Variable nodes (VNs) and check nodes (CNs) involve compression operations designed using the information bottleneck method to maximize preserved mutual information between code bits and quantized messages. We introduce alignment regions that assign the messages to groups with aligned reliability levels to decrease the number of individual design parameters. Group compositions with degree-specific separation of messages improve performance by up to 0.4 dB. Further, we generalize our recently proposed CN-aware quantizer design to irregular LDPC codes and layered schedules. The method optimizes the VN quantizer to maximize preserved mutual information at the output of the subsequent CN update, enhancing performance by up to 0.2 dB. A schedule optimization modifies the order of layer updates, reducing the average iteration count by up to 35 %. We integrate all new techniques in a rate-compatible decoder design by extending the alignment regions along a rate-dimension. Our complexity analysis shows that 2-bit decoding can double the area efficiency over 4-bit decoding at comparable performance.