In recent years, many communication standards have adopted the LDPC (Low-Density Parity Check) code due to its excellent error correction performance, but it also induces some problems. For example, the use of 5G in mobile phones dramatically reduces battery life. Therefore, it is particularly significant for LDPC code to design a decoding algorithm that does not increase hardware implementation complexity but has superior error correction performance and iteration speed faster than traditional decoding algorithms. Inspired by several network structures in artificial intelligence, bias is used to improve the performance and robustness of the network. In order to enhance decoding algorithm robustness and accuracy, a method is shown by changing the offset in OMSA to the bias and combining NMSA in the near-zero range in this paper. It significantly avoids the log-likelihood ratio information loss when less than the offset value and diminishes too quickly or sluggishly. A Segmented Bias/Normalize Min-Sum(SB/NMS) LDPC decoding algorithm is proposed with a layered structure. This algorithm can avoid the impact of the problems mentioned above and significantly improve the performance and iteration speed of the decoding process. Compared with the BLER (resp. BER) performance the traditional BP, NMS and OMS algorithm achieves a gain of 0.04, 0.11, and 0.15dB (resp. 0.035dB, 0.06, and 0.13dB). Meanwhile, the minimum SNR requirements of BLER =0.001 can be reduced by 0.02 dB compared with the BP algorithm. The parameters of SN/NMSA can be pre-processed on the computer, so there will be no additional increase in the overhead in resources and get better performance while getting faster iteration speed, while greatly guaranteeing the reliability and effectiveness of data transmission.
In recent years, many communication standards have adopted the LDPC (Low-Density Parity Check) code due to its excellent error correction performance, but it also induces some problems. For example, the use of 5G in mobile phones dramatically reduces battery life. Therefore, it is particularly significant for LDPC code to design a decoding algorithm that does not increase hardware implementation complexity but has superior error correction performance and iteration speed faster than traditional decoding algorithms. Inspired by several network structures in artificial intelligence, bias is used to improve the performance and robustness of the network. In order to enhance decoding algorithm robustness and accuracy, a method is shown by changing the offset in OMSA to the bias and combining NMSA in the near-zero range in this paper. It significantly avoids the log-likelihood ratio information loss when less than the offset value and diminishes too quickly or sluggishly. A Segmented Bias/Normalize Min-Sum(SB/NMS) LDPC decoding algorithm is proposed with a layered structure. This algorithm can avoid the impact of the problems mentioned above and significantly improve the performance and iteration speed of the decoding process. Compared with the BLER (resp. BER) performance the traditional BP, NMS and OMS algorithm achieves a gain of 0.04, 0.11, and 0.15dB (resp. 0.035dB, 0.06, and 0.13dB). Meanwhile, the minimum SNR requirements of BLER =0.001 can be reduced by 0.02 dB compared with the BP algorithm. The parameters of SN/NMSA can be pre-processed on the computer, so there will be no additional increase in the overhead in resources and get better performance while getting faster iteration speed, while greatly guaranteeing the reliability and effectiveness of data transmission.
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.
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.
Offset Min-Sum Algorithm (OMSA) and Normalized Min-Sum Algorithm (NMSA) are widely used in commercial LDPC decoders due to low complexity and reasonable performance. In this paper we proposes an Adaptive Layered Offset min- sum algorithm for the decoding of LDPC codes, which utilizes an adaptive offset factor to improve the accuracy of the soft information transferred during the iterative decoding process, and it provides good performance accordingly. The performed simulations showed that the layered offset min-sum decoding for LDPC codes can provide significant improvement compared to existing MS based algorithm, OMSA and NMSA.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
Low-density parity-check code (LDPC) is a kind of better error correction code which is played an important role in the reliability transmission of communication systems. In the aspect of decoding algorithm, the NMS algorithm becomes the mainstream algorithm dues to its lower complexity. what’s more, the Semi-serial decoding algorithm was put forward to reduce decoding iterations. However, the compensation factor of NMS algorithm is a fixed value and the Semi-serial decoding algorithm only considers one aspect of reducing iterations. In the actual decoding process, this value varies with the degree of the check node and the number of iterations. in order to solve the problems of these algorithms, this paper will propose a new improved algorithm. Firstly, we will adopt a dynamic compensation factor to improve performance of NMS algorithm on regular LDPC code. Then combined with the idea of Semi-serial decoding algorithm to reduce the number of iterations. The dynamic factor is firstly analyzed theoretically by density evolution theory. Then through the Monte Carlo experiment and the true LLR, the suitable dynamic compensation factors can be obtained which is changes with the number of iterations.