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arXiv:2102.03828 · IEEE Journal on Selected Areas in Communications

Learning to Decode Protograph LDPC Codes

Jincheng Dai, Kailin Tan, Zhongwei Si, Kai Niu, Mingzhe Chen, H. Vincent Poor, Shuguang Robert Cui

Published May 10, 2021• 80 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/jsac.2021.3078488

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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.
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.
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 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.
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.
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.