The paper carries out an in-depth investigation on the neural decoder design for protograph low-density parity-check (LDPC) codes. To be specific, based on the model-driven method, we propose a new type of protograph neural decoder with the parallel network (ParNet) decoding structure, called neural shuffled offset min-sum (NSOMS) decoder. The ParNet uses the model-driven method to unfold shuffled LDPC decoding algorithms into the interpretable network. Furthermore, with the aid of the over-estimation value (OEV), we optimize the training method to accelerate the convergence speed of the proposed decoding network. Theoretical and simulation results indicate that the proposed NSOMS decoder exhibits desirable performance compared to the state-of-the-art counterparts. Hence, the proposed NSOMS decoder can be regarded as a terrific solution for high-reliability communications.
The paper carries out an in-depth investigation on the neural decoder design for protograph low-density parity-check (LDPC) codes. To be specific, based on the model-driven method, we propose a new type of protograph neural decoder with the parallel network (ParNet) decoding structure, called neural shuffled offset min-sum (NSOMS) decoder. The ParNet uses the model-driven method to unfold shuffled LDPC decoding algorithms into the interpretable network. Furthermore, with the aid of the over-estimation value (OEV), we optimize the training method to accelerate the convergence speed of the proposed decoding network. Theoretical and simulation results indicate that the proposed NSOMS decoder exhibits desirable performance compared to the state-of-the-art counterparts. Hence, the proposed NSOMS decoder can be regarded as a terrific solution for high-reliability communications.
The paper designs a novel neural shuffled min-sum (NSMS) decoder with the model-driven deep learning method to achieve higher efficient and lower complexity decoding for protograph low-density parity-check (LDPC) codes. We propose a new type of customized branched neural network (CBNN) structure, which integrates shuffled min-sum (SMS) decoding algorithm and shuffled belief-propagation (SBP) decoding algorithm. In such a network structure, we can adjust layer arrangement and simplify parameter groups at a specific stage (i.e., training or inference stage) to reduce the unwarranted computational workload. Furthermore, we utilize the branched neuron mean difference (BNMD) to optimize the training targets of the proposed NSMS decoder, which significantly accelerates the convergence speed of the network. Analytical and simulation results show that the proposed NSMS decoder can achieve better performance than the state-of-the-art counterparts in terms of convergence speed, error rate and computational 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 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.
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.
With the rapid development of deep learning and its applications in physical layer communication, deep learning-based channel coding has gradually become a research hotspot. In this paper, based on the neural offset min-sum (NOMS) low-density parity-check (LDPC) decoding network, we propose a neural adaptive offset min-sum (NAOMS) LDPC decoding network. By considering the current input values of the check nodes when learning the additive offset parameters and introducing an adaptive offset weight vector, we can better leverage deep learning techniques. Experimental results show that, with a slight increase in complexity, the proposed decoder achieves a 0.8dB improvement in bit error rate (BER) over the NOMS LDPC decoding network. Moreover, the NAOMS decoder requires fewer learning offset parameters compared to the NOMS decoder.
With the applications of deep learning networks booming in physical layer communication, deep-learning-based channel decoding methods have become a research hotspot. However, the high complexity hinders the application of deep neural network (DNN) on long code. In this paper, we propose a model-driven deep learning method for normalized min-sum (NMS) low-density parity-check (LDPC) decoding. First, we propose a neural normalized min-sum (NNMS) LDPC decoding network. By unfolding the iterative decoding progress between checking nodes (CNs) and variable nodes (VNs) into a feedforward propagation network, we can make use of the advantages of both model-driven deep learning methods and conventional normalized min-sum (CNMS) LDPC decoding method. Second, considering that the NNMS decoder needs large number of multipliers, we propose a shared neural normalized min-sum (SNNMS) decoding network to reduce the number of correction factors. Experimental results show that the BER performance of the proposed NNMS decoder is 1.5dB better than the conventional LDPC decoder, using fewer iterations. Furthermore, the proposed SNNMS decoder outperforms the proposed NNMS decoder and reduces the computation complexity.