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International Wireless Communications and Mobile Computing Conference (IWCMC)

A Deep Learning based Multi-edge-type decoding algorithm for 5G NR LDPC codes

Tianyu Du, Hao Ju, Yin Xu, Dazhi He, Wenjun Zhang

Published Jun 19, 2023• 6 citations
Publisher

Abstract

Low-density parity-check(LDPC) code has been selected as the channel coding method by 5G NR because of its excellent error-correcting performance. To further improve the performance of LDPC decoding, this paper proposes a neural normalized min-sum(NNMS) algorithm based on multi-edge-type(MET). Based on the LLR convergence analysis of the protograph matrix of 5G NR, the base matrix is divided into several independent regions. Each part is assigned a unique scaling factor at different iterations. To verify the effectiveness of the proposed algorithm, We use two parity-check matrixes(PCM) derived from different base graphs in simulations. The results show that the proposed algorithm performs at most 0.45dB better than BP, 0.37dB better than NMS, and 0.25dB better than OMS, respectively, when the frame error rate (FER) is at 1$0^{-5}$ level over additive white Gaussian noise (AWGN) channels using BPSK modulation.

DOI
10.1109/iwcmc58020.2023.10182649

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Low-density parity-check(LDPC) code has been selected as the channel coding method by 5G NR because of its excellent error-correcting performance. To further improve the performance of LDPC decoding, this paper proposes a neural normalized min-sum(NNMS) algorithm based on multi-edge-type(MET). Based on the LLR convergence analysis of the protograph matrix of 5G NR, the base matrix is divided into several independent regions. Each part is assigned a unique scaling factor at different iterations. To verify the effectiveness of the proposed algorithm, We use two parity-check matrixes(PCM) derived from different base graphs in simulations. The results show that the proposed algorithm performs at most 0.45dB better than BP, 0.37dB better than NMS, and 0.25dB better than OMS, respectively, when the frame error rate (FER) is at 10−50^{-5}0−5 level over additive white Gaussian noise (AWGN) channels using BPSK modulation.
Belief propagation (BP) provides the basis for the design of 5G new radio low density parity check (5G-NR LDPC) codes, which in turn require a BP-based decoding algorithm. The min-sum algorithm (MSA), the simplification of sum-product algorithm (SPA), should hardly be regarded as a BP-based decoding algorithm because of its minimization. To remedy this, this paper adopts the multi-edge-type density evolution (MET-DE) as the main analysis tool, and introduces the concept of Kullback-Leibler divergence. Then the least Kullback-Leibler divergence criterion is proposed to identify the optimal normalization factors. Finally, Density-Evolution-aided Adaptive Normalization Min-Sum Algorithm (DE-aided ANMSA) with edge classification is further proposed for the decoding implementation of 5G-NR LDPC codes. Simulation results demonstrate that the proposed decoding algorithm can achieve excellent performance, while the greatest advantage is that its factors could be obtained more flexibly and accurately than traditional training methods. In addition, the optimal factors for base graph 2 in 5G-NR LDPC codes are provided as well.
The success of deep learning has encouraged its applications in decoding error-correcting codes, e.g., LDPC decoding. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding, namely neural NMS (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feed-forward propagation network, we can harvest the benefits of both the model-driven deep learning and the conventional normalized min-sum (NMS) LDPC decoding method. In addition, we proposed a shared parameters NNMS with the LeakyReLU and a 12-bit quantizer (SNNMS-LR-Q) which reduces the number of required multipliers and correction factors by sharing parameters, increasing the nonlinear fitting ability by adding LeakyReLU. By utilizing the 12-bit quantizer, we can improve the confrontation ability. Thorough experiments with different code lengths, code rates, channel conditions, and check matrices are implemented to demonstrate the advantages and robustness of our proposed networks. The BER performance of the proposed NNMS is 1.5 dB better than the NMS, using fewer iterations. Meanwhile, The SNNMS-LR-Q outperforms the NNMS regarding the BER performance and efficiency.
LDPC code is a widely-used high-performance error correction code. In recent years, LDPC decoding based on deep learning and neural networks becomes a research hotspot. Based on the (512,256) LDPC code of the CCSDS standard, this paper firstly studies the traditional decoding algorithms of SP, MS, NMS, and OMS, laying a foundation for the construction of neural networks. Then a data-driven (DD) decoding method is studied which adopts the information with its encoded, modulated and noise-added LDPC code as the training data within a Multi-layer Perceptron (MLP) neural network. In order to solve the problem of high bit error rate (BER) in data-driven method, the Neural Normalized Min-sum (NNMS) decoding in which the NMS algorithm is mapped to the neural network structure is proposed, achieving more excellent BER performance than that of NMS. The BER declines by 85.19% when channel SNR equals to 3.5 dB. Finally, improved training methods to enhance the SNR generalization ability of the NNMS network is studied.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.
To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10-4level over additive white Gaussian noise (AWGN) channels using QPSK modulation.
Abstract In order to cater to the needs of the 5G standard, one of the prominent solutions in terms of high coding gain, high throughput and low power dissipation is the 5G NR LDPC (New Radio Low Density Parity Check) codes which have been adopted by 5G Standard. LDPC codes are the successful Third Generation Forward Error Correcting codes. An Efficient decoder is the key to the success of any Error Correcting Code. LDPC codes are one whose parity check matrix have a very few non zero entries. 5G NR LDPC codes are constructed by Protographs or base graphs and are block structured. This paper improves the performance of Layered Iterative minsum Approximation Message Passing decoding Algorithm using Rate Matching, Fixed Point Quantization and Offset minsum techniques. Rate Matching is to maintain the exact number of encoded blocks with in the TTI. Simulation of this algorithm with BPSK encoding over AWGN channel shows that BER of 10-3 gives Eb/No of~2 dB for the block length of 105.