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 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.
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.
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.
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.
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.
The min-sum (MS) decoding for low-density parity-check codes, though less complex than the sum–product algorithm, suffers from worse error-correcting performance. For enhancement, neural MS decoders leveraging deep learning have recently been introduced, but how to train them has not been sufficiently discussed. In this paper, we propose a novel dataset construction method and also propose systematic learning strategies by finding a good combination of dataset composition, loss functions, weight sharing, weight assignment , and weight update method. Simulations demonstrate that the proposed method achieves better error-correcting performance than other works, especially in the error floor region, within a limited number of iterations.
Recently a number of low-density parity-check (LDPC) decoding algorithms based on deep learning have been proposed in the literature. However, most of the work has been targeted for additive white Gaussian noise (AWGN) channels. For more practical scenarios, in this paper we investigate the neural-network based min-sum (MS) decoding for protograph LDPC codes in fading channels. Since the wireless channel is complex and varying, accurate channel state information (CSI) cannot be always available at the receiver. We classify the scenarios into three cases with perfect CSIs, imperfect CSIs, and no CSIs. By assigning learnable weights on the edges in the iterative decoding, the proposed neural decoder compensates for the performance loss caused by the error/lack of CSIs. The trajectory-based extrinsic information transfer (T-EXIT) chart is employed as a theoretical tool to select the proper training dataset for the neural network and the proper channel initialization scheme for the receiver. Numerical results in terms of block error rates are provided, which agree with the T-EXIT analysis. It can be seen that the proposed neural MS decoder clearly outperforms the traditional MS algorithm in Rayleigh fading channels. Meanwhile, the proposed decoder shows a good compatibility so that it can be applied to the cases with different accuracy of CSIs.