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Journal of Communications and Networks

NOLD: A neural-network optimized low-resolution decoder for LDPC codes

Lei Chu, Huanyu He, Ling Pei, Robert C. Qiu

Published Jun 1, 2021• 12 citations
Publisher

Abstract

The min-sum (MS) algorithm can decode Low-density parity-check (LDPC) codes with low computational complexity at the cost of slight performance loss. It is an effective way to realize hardware implementation of the min-sum decoder by quantizing the floating belief messages (i.e., check-to-variable messages and variable-to-check messages) into low-resolution (i.e., 2–4 bits) versions. However, such a way can lead to severe performance degradation due to the finite precision effect. In this paper, we propose a neural-network optimized low-resolution decoding (NOLD) algorithm for LDPC codes to deal with the problem. Specifically, the optimization of decoding parameters (i.e., scaling factors and quantization step) is achieved in a hybrid way, in which we concatenate a NOLD decoder with a customized neural network. All learnable parameters associated with the decoding parameters are assigned to each neuron in the proposed method. What's more, we design a new activation function whose outputs are close to the employed quantizer ones when network parameters are finally optimized off-line. Finally, the performance of the proposed method is verified by numerous experiments. For the case of 2-bit decoding, the proposed approach significantly outperforms several conventional decoders at the expense of slightly increased off-line training time. Besides, the proposed method with 4-bit quantization incurs only 0.1 dB performance loss compared with the floating min-sum decoder at the coded bit-error-rate of 10−5. Moreover, we show that the proposed NOLD decoder works over a wide range of channel conditions for regular and irregular LDPC codes. Simulation code for reproductive results is publicly available1.

DOI
10.23919/jcn.2021.000014

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The min-sum (MS) algorithm can decode Low-density parity-check (LDPC) codes with low computational complexity at the cost of slight performance loss. It is an effective way to realize hardware implementation of the min-sum decoder by quantizing the floating belief messages (i.e., check-to-variable messages and variable-to-check messages) into low-resolution (i.e., 2–4 bits) versions. However, such a way can lead to severe performance degradation due to the finite precision effect. In this paper, we propose a neural-network optimized low-resolution decoding (NOLD) algorithm for LDPC codes to deal with the problem. Specifically, the optimization of decoding parameters (i.e., scaling factors and quantization step) is achieved in a hybrid way, in which we concatenate a NOLD decoder with a customized neural network. All learnable parameters associated with the decoding parameters are assigned to each neuron in the proposed method. What's more, we design a new activation function whose outputs are close to the employed quantizer ones when network parameters are finally optimized off-line. Finally, the performance of the proposed method is verified by numerous experiments. For the case of 2-bit decoding, the proposed approach significantly outperforms several conventional decoders at the expense of slightly increased off-line training time. Besides, the proposed method with 4-bit quantization incurs only 0.1 dB performance loss compared with the floating min-sum decoder at the coded bit-error-rate of 10−5. Moreover, we show that the proposed NOLD decoder works over a wide range of channel conditions for regular and irregular LDPC codes. Simulation code for reproductive results is publicly available1.
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.
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.
This paper analyzes the performance of quantized min-sum decoding algorithms for irregular low-density parity-check (LDPC) codes. For regular LDPC codes, it is known that the normalized or offset min-sum decoding algorithm with quantization bits less than 6 bits achieves good performances over wide range of signal-to-noise ratios (SNR). However, finite precision effects in decoding irregular LDPC codes are different from that in decoding regular LDPC codes which is caused by the difference of convergence speeds between low degree nodes and high degree nodes. This paper proposes a novel method to improve the performance of the conventional normalized or offset min-sum decoding algorithm when it is approximated with finite precision for hardware implementations. The proposed method applies down-scaling factors to intrinsic information which has effects on increasing the reliability of extrinsic information at variable nodes and compensating the quantization errors caused by finite precision. Computer simulation results for irregular LDPC codes show that the proposed normalized and offset min-sum decoding algorithms achieve better performances at high SNR compared to the conventional normalized and offset min-sum algorithms under (6:2) quantization scheme.
In this paper, we discuss the perspectives of utilizing deep neural networks (DNN) to decode Low-Density Parity Check (LDPC) codes. The main idea is to build a neural network to learn and optimize a conventional iterative decoder of LDPC codes. A DNN is based on Tanner graph, and the activation functions emulate message update functions in variable and check nodes. We impose a symmetry on weight matrices which makes it possible to train the DNN on a single codeword and noise realizations only. Based on the trained weights and the bias, we further quantize messages in such DNN-based decoder with 3-bit precision while maintaining no loss in error performance compared to the min-sum algorithm. We use examples to present that the DNN framework can be applied to various code lengths. The simulation results show that, the trained weights and bias make the iterative DNN decoder converge faster and thus achieve higher throughput at the cost of trivial additional decoding complexity.
In this paper, we introduce a method of using quantized neural networks (QNN) to design finite alphabet message passing decoders (FAID) for Low-Density Parity Check (LDPC) codes. Specifically, we construct a neural network with low precision activations to optimize a FAID over Additive White Gaussian Noise Channel (AWGNC). The low precision activations cause a critical issue that their gradients vanish almost everywhere, making it difficult to use classical backward propagation. We introduce straight-through estimators (STE) to avoid this problem, by replacing zero derivatives of quantized activations with surrogate gradients in the chain rules. We present a systematic approach to train such networks while minimizing the bit error rate, which is a widely used and accurate metric to measure the performance of iterative decoders. Examples and simulations show that by training a QNN, a FAID with 3-bit of message and 4-bit of channel output can be obtained, which performs better than the more complex floating-point minsum decoding algorithm. This methodology is promising in the sense that it facilitates designing low-precision FAID for LDPC codes while maintaining good error performance in a flexible and efficient manner.
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.