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IEEE Access

Decoding Optimization for 5G LDPC Codes by Machine Learning

Xiaoning Wu, Ming Jiang, Chunming Zhao

Published Jan 1, 2018• 69 citations
Publisher

Abstract

In this paper, we propose a generalized minimum-sum decoding algorithm using a linear approximation (LAMS) for protograph-based low-density parity-check (PB-LDPC) codes with quasi-cyclic (QC) structures. The linear approximation introduces some factors in each decoding iteration, which linearly adjust the check node updating and channel output. These factors are optimized iteratively using machine learning, where the optimization can be efficiently solved by a small and shallow neural network with training data produced by the LAMS decoder. The neural network is built according to the parity check matrix of a PB-LDPC code with a QC structure which can greatly reduce the size of the neural network. Since, we optimize the factors once per decoding iteration, the optimization is not limited by the number of the iterations. Then, we give the optimized results of the factors in the LAMS decoder and perform decoding simulations for PB-LDPC codes in fifth generation mobile networks (5G). In the simulations, the LAMS algorithm shows noticeable improvement over the normalized and the offset minimum-sum algorithms and even better performance than the belief propagation algorithm in some high signal-to-noise ratio regions.

DOI
10.1109/access.2018.2869374

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In this paper, we propose a generalized minimum-sum decoding algorithm using a linear approximation (LAMS) for protograph-based low-density parity-check (PB-LDPC) codes with quasi-cyclic (QC) structures. The linear approximation introduces some factors in each decoding iteration, which linearly adjust the check node updating and channel output. These factors are optimized iteratively using machine learning, where the optimization can be efficiently solved by a small and shallow neural network with training data produced by the LAMS decoder. The neural network is built according to the parity check matrix of a PB-LDPC code with a QC structure which can greatly reduce the size of the neural network. Since, we optimize the factors once per decoding iteration, the optimization is not limited by the number of the iterations. Then, we give the optimized results of the factors in the LAMS decoder and perform decoding simulations for PB-LDPC codes in fifth generation mobile networks (5G). In the simulations, the LAMS algorithm shows noticeable improvement over the normalized and the offset minimum-sum algorithms and even better performance than the belief propagation algorithm in some high signal-to-noise ratio regions.
This thesis investigates the optimization of Low-Density Parity-Check (LDPC) decoding through machine learning techniques, with a specific focus on 5G communication systems. Traditional LDPC decoding algorithms face a critical trade-off: Belief Propagation (BP) offers excellent error-correction performance but with high computational complexity, while Min-Sum (MS) reduces complexity at the cost of degraded performance. To address this limitation, a hybrid neural network architecture is proposed that incorporates learnable normalization and offset weights into the message-passing framework of LDPC decoders. This approach integrates multiplicative (normalization) and additive (offset) weights into the Tanner graph structure, allowing the decoder to adapt to specific channel conditions. A novel weighted binary cross-entropy loss function is developed that prioritizes entire block recovery by assigning different importance to information and parity bits during training. Experimental results demonstrate that ML-assisted decoder consistently outperforms conventional Min-Sum decoding, approaching the error-correction capability of Belief Propagation while maintaining comparable computational efficiency to Min-Sum. Comprehensive evaluations across different weight configurations (scalar and vector-based) reveal that increased parametrization generally improves decoding performance. Analysis of the impact of iteration counts shows that the optimal number of decoding iterations varies between different code configurations with studied Basegraph 1 case requiring 15 iterations for optimal performance while studied Basegraph 2 case benefits significantly from 20 iterations. The proposed ML-assisted LDPC decoder represents a significant advancement for 5G systems, offering improved error correction at lower signal strengths while balancing latency and computational requirements. This research contributes to the ongoing evolution of wireless technology by demonstrating how machine learning can effectively enhance traditional decoding algorithms, providing a practical pathway toward more efficient and adaptive error correction in modern communication systems.
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.
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with the codelength, thus they can only support short to moderate codelengths. From the point view of practicality, we propose a high-performance neural min-sum (MS) decoding method that makes full use of the lifting structure of protograph low-density parity-check (LDPC) codes. By this means, the size of the parameter array of each layer in the neural decoder only equals the number of edge-types for arbitrary codelengths. In particular, for protograph LDPC codes, the proposed neural MS decoder is constructed in a special way such that identical parameters are shared by a bundle of edges derived from the same edge-type. To reduce the complexity and overcome the vanishing gradient problem in training the proposed neural MS decoder, an iteration-by-iteration (i.e., layer-by-layer in neural networks) greedy training method is proposed. With this, the proposed neural MS decoder tends to be optimized with faster convergence, which is aligned with the early termination mechanism widely used in practice. To further enhance the generalization ability of the proposed neural MS decoder, a codelength/rate compatible training method is proposed, which randomly selects samples from a set of codes lifted from the same base code. As a theoretical performance evaluation tool, a trajectory-based extrinsic information transfer (T-EXIT) chart is developed for various decoders. Both T-EXIT and simulation results show that the optimized MS decoding can provide faster convergence and up to 1dB gain compared with the plain MS decoding and its variants with only slightly increased complexity. In addition, it can even outperform the sum-product algorithm for some short codes.
A hybrid decoding algorithm for low-density parity-check codes is presented. The proposed algorithm applies different updating schemes, such as the normalized min-sum (NMS) simplification and linear approximation, to the check-node based on its degree. Meanwhile, to eliminate the dependence on the channel variance estimation, the proposed algorithm adopts a multiplicative factor to initialize the channel input and a fixed linear functions for check-node updating. From the iterative thresholds and decoding simulations, our proposed algorithm can be shown to achieve improved performance (much closer to that of the belief propagation decoding) at the expense of a slight increase in complexity to NMS algorithm.
In this letter, we propose various low-complexity neural layered min-sum (NLMS) algorithms to improve the decoding performance of the fifth generation (5G) new radio (NR) low-density parity-check (LDPC) codes. Our proposals are based on the computationally-efficient normalized offset min-sum (NOMS) approach for the layered belief propagation (LBP). The main novelty of our proposals is a deep neural network (DNN) that implements the layered mode decoding and that additionally learns the normalization and the offset parameters of the NOMS scheme. The schemes that we propose use the DNN as well as adaptation and filtering for estimating the optimum values of these parameters. We show by simulation that our proposed decoders achieve a significant computational benefit compared to the standard (non-neural) LBP decoder without an appreciable performance penalty.
The use of neural networks is advancing across several fields, particularly in digital communications. However, in the domain of error-correcting codes, the prevailing consensus is that Artificial Intelligence (AI) tools can, at best, match the performance of existing methods without offering any significant simplifications or improvements. As a result, the initial enthusiasm for AI-based approaches in this area has substantially declined. Recently, however, it has been demonstrated that gradient descent can be used to guide the optimization process for the code construction of unstructured Low-Density Parity-Check (LDPC) codes. In this paper, we extend and generalize this method to also optimize Quasi-Cyclic LDPC codes (QC-LDPC). More specifically, we propose to apply the new method directly to the base protograph structures of QC-LDPC codes standardized in the fifth generation (5G) New Radio (NR) framework. Experimental results reveal that, for small protograph matrices, the proposed optimization process achieves significant coding gains, with improvements of up to 1.2 dB in signal-to-noise ratio (SNR) at a target frame error rate (FER) of 10−2.