Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to cyclic and QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the cyclic structure and section-wise cyclic structure inherent in cyclic and QC-LDPC codes respectively, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various cyclic and QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.
Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to cyclic and QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the cyclic structure and section-wise cyclic structure inherent in cyclic and QC-LDPC codes respectively, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various cyclic and QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.
Recently, deep learning has demonstrated improvements over classical decoding algorithms in various families of error-correcting codes with short to moderate block lengths. Neural decoders like neural belief propagation (NBP), constructed based on the Tanner graphs of linear codes, have been extensively studied, but their application to longer codes is limited due to increased network complexity with longer block lengths. This complexity leads to higher computational costs and deployment challenges, such as GPU memory usage. To address this, we propose a novel revolving framework for NBP-like decoders tailored to QC-LDPC codes, a commonly used class of error correction codes. Our approach leverages the section-wise cyclic structure inherent in QC-LDPC codes, significantly simplifying the complexity of the network. Experimental results demonstrate the effectiveness of our method across various QC-LDPC codes. Especially, compared to the traditional decoding scheme based on the section-wise cyclic structure, our proposed decoder shows substantial improvements on 5G LDPC codes, exhibits better performance than the traditional min-sum decoder, and approaches the sum-product decoder without a noticeable error floor within the investigated noise levels.
For short to moderate-length block codes, neural belief propagation (NBP) decoders are developed to ameliorate the performance of the belief propagation algorithm (BPA). The core concept underlying these decoders is to model belief propagation (BP) as a neural network, allowing adaptable decoding through trainable weights. The article proposes a novel Gated neural min-sum (GNMS) decoding technique with learnable parameters as a more hardware-efficient substitute for conventional NBP decoders. By using parameterised updates and gating techniques, our approach reformulates the min-sum (MS) algorithm, which is an approximation of BP, while preserving the flexibility of neural approaches and drastically lowering computing overhead. Additionally, we develop an autoencoder-assisted framework that supports flexible, learning-based optimisation for GNMS and Gated Neural Offset Min-Sum (GNOMS) decoders. The suggested decoders achieve error-correction performance at par with the most advanced NBP decoders by evaluating them on a variety of short to moderate-length block codes. Notably, when compared to traditional BP, the suggested approach lowers the bit error rate (BER) 10-fold for signal-to-noise ratio (SNR) greater than 3 dB. Furthermore, the efficacy of the proposed work is exhibited by comparing the computational complexity of the neural network-based decoders, highlighting the advantages in terms of practical implementation and hardware feasibility. The simulation results demonstrate that GNMS decoding with learnable parameters offers a convincing trade-off between complexity and performance, offering a potential path for future decoder design in contemporary communication systems.
We investigate the application of machine learning techniques (in particular, deep neural networks, DNN) to improve the decoding algorithms of short quasi-cyclic low-density paritycheck (LDPC) codes adopted to the 5G standard. We note that straightforward application of general-purpose DNNs is not possible due to the curse of dimensionality problem – the training set size grows exponentially with the number of information bits. In our opinion, the only way to deal with this problem is to combine deep learning methods with existing decoding algorithms. We start with a Tanner-based neural network decoder with Min-Sum activation functions proposed by Nachmani et al. and extend it as follows. First, the quasi-cyclic nature of 5G LDPC codes allows us to use a single weight per circular matrix (circulant). We refer to this as weight sharing. This idea significantly reduces the training time, preserving the error-correcting performance. Second, we add residual connections to our NN architecture. Residual connections improve the performance and reduce the training time. We also present the results for the rate and length adaptation techniques. Rate adaptation allows multiple DNNs corresponding to different coding rates to run with a single set of trained weights. Length adaptation allows optimally reusing weights for multiple lifting size indices.
Neural belief propagation (NBP) decoding can improve the performance of belief propagation (BP) decoding for high-density parity check (HDPC) codes, at the expense of higher memory storage requirement and computational complexity due to the addition of trainable weight coefficients. To reduce the high storage requirement of NBP, the cyclically equivariant neural BP (CENBP) algorithm makes full use of the cyclically invariant property of the cyclic code, optimizes and reuses the weight coefficients of the NBP algorithm, at the expense of further increasing the computational complexity of NBP. In this paper, we propose low-complexity, in terms of both memory storage requirement and computational complexity, NBP and CENBP decoding algorithms based on Tensor Ring (TR) decomposition. First, in order to reduce the memory storage and computational complexity of the NBP algorithm, we propose a TR-based compression algorithm to compress the messages and mathematical calculations in the NBP decoding algorithm, called TR-NBP algorithm. Second, to address the high computational complexity of the CENBP algorithm, we propose to apply TR decomposition-based compression to the odd layers of the CENBP decoding algorithm, called TR-CENBP, to reduce the computational complexity, and further reduce the required memory storage requirement of the CENBP algorithm. Furthermore, we use TR decomposition-based compression to simplify the mathematical computations associated with thetanhfunction in the NBP algorithm to further reduce the complexity of the hardware implementation. Experimental results show that direct compression of BP algorithm using TR decomposition results in significant performance degradation and our proposed low complexity TR-NBP algorithm and TR-CENBP algorithm can greatly reduce both the memory storage requirement and computation complexity, without significant performance degradation for typical BCH and LDPC codes.
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.
BP decoding algorithm is one of the commonly used decoding algorithms for LDPC codes. To adapt LDPC codes to different 5G scenarios and further improve the decoding performance of short LDPC codes, a scheme combining model-driven deep learning with a traditional BP decoding algorithm is proposed. With the advantages of model-driven, this solution expands the decoding iteration process between the check node and the variable node into a neural network and proposes a parameter normalization optimization solution to solve the problem of the program with many training parameters, the edge weights of the optimized Tanner graph are re-assigned and bound. Simulation results show that the proposed scheme can improve the decoding performance of LDPC codes with short lengths.