We propose a neural min-sum (MS) decoder for non-binary LDPC codes by applying deep learning to the decoding with short to moderate code lengths. In this algorithm, the iterations are unfolded into hidden layers of the neural network, and trainable weights are added to the check node updates to mitigate the correlation in the message passing due to short girths in the Tanner graph. To avoid gradient vanishing and to converge faster, we adopt an iterative training mechanism for parameter tuning. Furthermore, we investigate the impact of girth distribution on the proposed neural MS decoder, which reveals the reasons for the expected performance improvement. Numerical results in terms of bit error rate are provided, which show that the neural MS decoder achieves significant gains for decoding non-binary LDPC codes.
We propose a neural min-sum (MS) decoder for non-binary LDPC codes by applying deep learning to the decoding with short to moderate code lengths. In this algorithm, the iterations are unfolded into hidden layers of the neural network, and trainable weights are added to the check node updates to mitigate the correlation in the message passing due to short girths in the Tanner graph. To avoid gradient vanishing and to converge faster, we adopt an iterative training mechanism for parameter tuning. Furthermore, we investigate the impact of girth distribution on the proposed neural MS decoder, which reveals the reasons for the expected performance improvement. Numerical results in terms of bit error rate are provided, which show that the neural MS decoder achieves significant gains for decoding non-binary LDPC codes.
In this paper, we discuss the perspectives of utilizing deep neural networks (DNN) to decode Low-Density Parity Check (LDPC) codes. The main idea is to build a neural network to learn and optimize a conventional iterative decoder of LDPC codes. A DNN is based on Tanner graph, and the activation functions emulate message update functions in variable and check nodes. We impose a symmetry on weight matrices which makes it possible to train the DNN on a single codeword and noise realizations only. Based on the trained weights and the bias, we further quantize messages in such DNN-based decoder with 3-bit precision while maintaining no loss in error performance compared to the min-sum algorithm. We use examples to present that the DNN framework can be applied to various code lengths. The simulation results show that, the trained weights and bias make the iterative DNN decoder converge faster and thus achieve higher throughput at the cost of trivial additional decoding complexity.
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.
In this paper, layered min-sum (MS) iterative decoding is formulated as a customized neural network following the sequential scheduling of check node (CN) updates. By virtue of the lifting structure of protograph low-density parity-check (LDPC) codes, identical network parameters are shared among all derived edges originating from the same edge in the protograph, which makes the number of learn- able parameters manageable. The proposed neural layered MS decoder can support arbitrary codelengths consequently. Moreover, an iteration-wise greedy training method is proposed to tune the parameters such that it avoids the vanishing gradient problem and accelerates the decoding convergence.
In this work, we propose a neural adjusted min-sum (NAMS) decoder for low-density parity-check (LDPC) codes. In particular, we improve the traditional normalized min-sum (NMS) decoder by introducing a selection mechanism to adjust the check-node update step, where either the min-sum rule or the belief propagation (BP) rule is selected. Besides, we unfold the modified decoder into a model-driven neural network, where layer-dependent trainable parameters are introduced as weights in the Tanner graph and optimized by gradient descent-based methods during network training. Simulation results demonstrate that the proposed NAMS decoder is able to provide superior error-correction performance as compared to the neural NMS decoder, with only slightly increased computational complexity. Moreover, in certain circumstances, the proposed NAMS decoder even outperforms the neural BP decoder, with much lower computational complexity.
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.
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.