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 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 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.
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 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.
Deep learning-based decoding algorithms have emerged as a focal point currently in contemporary research. Neural Offset Min-Sum Belief Propagation decoding algorithm is one of the traditional deep learning methods rooted in model-driven approaches. However, with the gradual increase in codeword length, there is an inevitable surge in the training cost and time complexity of such kind of deep learning algorithms. Addressing this issue, a novel deep learning algorithm based on the structural characteristics of the base graph in protograph LDPC codes is proposed. By strategically training the base graph and introducing a unique bit decoding allocation strategy, we endeavor to harmonize the Deep Learning algorithm with the intrinsic structure of the base graph itself. This approach contrasts favorably with several existing methods that utilize conventional segmental deep learning decoding algorithms for protograph LDPC codes. Simulation results demonstrate that, compared to other model-driven based deep learning algorithms, the proposed algorithm significantly reduces the number of parameters required for storage and training, while the loss in decoding performance remains within acceptable bounds.
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.
For recent years, deep learning has been studied and utilized among decoders in wireless and optical communication. For low density parity check (LDPC) codes, most works use neural network (NN) to implement the belief propagation (BP) decoder and unfold its iterations into layers activated by different functions. However, the whole decoder composed by neural network performs lots of non-linear operations, which are time consuming and unfriendly to hardware implementation. In this work, a neural network-aided normalized min-sum (NN-aided NMS) decoder for LDPC code is proposed, in which the normalization factors are inferred from input log likelihood ratio (LLR) by apre-trained NN, while maintaining check and variable nodes processing the same as in min-sum (MS) decoder. In order to test the proposed decoder with irregular LDPC code, a rate-7/8 one was constructed using progressive edge growth (PEG) algorithm, showing better error correction capability than the standard of consultative committee for space data systems (CCSDS) LDPC (8176,7154) code by 0.08 dB with the same rate. Simulation results show that, NN-aided NMS decoder outperforms MS decoder by 0.3 dB, and its performance approaches BP decoder with a gap of 0.02 dB, which is 50% closer than the best NMS decoder using 0.7 as the normalization factor. The proposed decoder has good performance for both regular and irregular LDPC codes, and needs much less computation complexity than BP decoder. It introduces more linear computation than NMS decoder but achieves better bit error rate (BER) performance, thus becoming a good complement between BP and NMS decoder when trading off among complexity, error correction performance and hardware implementation for wireless and satellite communication.