Low-density parity-check (LDPC) codes are widely used in a variety of communication systems because of their low complexity iterative decoding and performance approaching Shannon capacity. However, the existence of error floor seriously hinders the application and development of LDPC codes in related fields. In this paper, a deep learning-aided post-processing scheme (DLAPPS) based on Layered Normalized Min-Sum algorithm (LNMSA) is proposed to effectively lower error floor of LDPC codes. LNMSA is used in the first stage, and in the second stage incorrect frames are re-decoded by processing two types of nodes classified by neural networks. Simulation results show that the proposed DLAPPS can significantly improve error correction performance and lower the error floor of LDPC codes while maintaining a relatively low decoding complexity.
Low-density parity-check (LDPC) codes are widely used in a variety of communication systems because of their low complexity iterative decoding and performance approaching Shannon capacity. However, the existence of error floor seriously hinders the application and development of LDPC codes in related fields. In this paper, a deep learning-aided post-processing scheme (DLAPPS) based on Layered Normalized Min-Sum algorithm (LNMSA) is proposed to effectively lower error floor of LDPC codes. LNMSA is used in the first stage, and in the second stage incorrect frames are re-decoded by processing two types of nodes classified by neural networks. Simulation results show that the proposed DLAPPS can significantly improve error correction performance and lower the error floor of LDPC codes while maintaining a relatively low decoding complexity.
Low-Density Parity-Check (LDPC) codes have extensive applications in numerous communication systems. However, iterative LDPC decoders may suffer from error floor. In this paper, a low complexity post processing scheme (PPS) is proposed to significantly improve the error correction performance of a Min-Sum based LDPC decoder in the error floor region. Instead of using trapping set elimination algorithms, the proposed PPS introduces perturbations so that a decoder can escape from undesired local maximums. After decoding failure, for these unreliable code bits, the proposed PPS generates carefully modified soft messages, which are employed in the following decoding iterations. Numerical results demonstrate that the presented PPS significantly lowers the error floor for simulated LDPC codes.
Low-density parity-check (LDPC) codes have been successfully commercialized in communication systems due to their strong error correction capabilities and simple decoding process. However, the error-floor phenomenon of LDPC codes, in which the error rate stops decreasing rapidly at a certain level, presents challenges for achieving extremely low error rates and deploying LDPC codes in scenarios demanding ultra-high reliability. In this work, we propose training methods for neural min-sum (NMS) decoders to eliminate the error-floor effect. First, by leveraging the boosting learning technique of ensemble networks, we divide the decoding network into two neural decoders and train the post decoder to be specialized for uncorrected words that the first decoder fails to correct. Secondly, to address the vanishing gradient issue in training, we introduce a block-wise training schedule that locally trains a block of weights while retraining the preceding block. Lastly, we show that assigning different weights to unsatisfied check nodes effectively lowers the error-floor with a minimal number of weights. By applying these training methods to standard LDPC codes, we achieve the best error-floor performance compared to other decoding methods. The proposed NMS decoder, optimized solely through novel training methods without additional modules, can be integrated into existing LDPC decoders without incurring extra hardware costs. The source code is available at https://github.com/ghy1228/LDPC_Error_Floor .
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.
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.
Low-density parity-check (LDPC) codes are of prime importance in achieving near-Shannon capacity in current communication systems. However, the optimal decoding process for LDPC codes is computationally intensive. This paper presents a neural normalized min-sum (NNMS) decoding network that improves error correction capabilities with minimal computational overhead. A weight-sharing approach is adopted in the NNMS model, in which the correction factors (α, β) are shared across nodes within a single layer. This approach decreases the total number of parameters in the model compared to traditional neural decoders, making it easier for hardware implementation. The NNMS model is tested using a (576, 432) LDPC code for an additive white Gaussian noise channel with binary phase shift keying modulation. Simulation results show that the NNMS model outperforms traditional normalized min-sum (NMS) decoders. At a signal-to-noise ratio of 5 dB, the NNMS model has a bit-error rate (BER) of 1.0 × 10−7, whereas traditional NMS models have a less steep slope. In particular, the NNMS model has a coding gain of 1.25 dB compared to the traditional NMS model at a BER threshold of 1.0 × 10−3. This shows that the NNMS model is an efficient solution for high-performance, real-time digital communication systems.
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.