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IEEE Access

Learning to Decode Polar Codes With One-Bit Quantizer

Jian Shu Gao, Kai Niu, Chao Dong

Published Jan 1, 2020• 10 citations
Publisher

Abstract

A deep learning method for improving the performance of polar belief propagation (BP) decoder equipped with a one-bit quantizer is proposed. The method generalizes the standard polar BP algorithm by assigning weights to the layers of the unfolded factor graph. These weights can be learned autonomously using deep learning techniques. We prove that the improved polar BP decoder has a symmetric structure, so that the weights can be trained by an all-zero codeword rather than an exponential number of codewords. In order to accelerate the training convergence, a layer-based weight assignment scheme is designed, which decreases the amount of trainable weights. Simulation results show that the improved polar BP decoder with a one-bit quantizer outperforms the standard polar BP decoder with a 2-bit quantizer and achieves faster convergence.

DOI
10.1109/access.2020.2971526

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A deep learning method for improving the performance of polar belief propagation (BP) decoder equipped with a one-bit quantizer is proposed. The method generalizes the standard polar BP algorithm by assigning weights to the layers of the unfolded factor graph. These weights can be learned autonomously using deep learning techniques. We prove that the improved polar BP decoder has a symmetric structure, so that the weights can be trained by an all-zero codeword rather than an exponential number of codewords. In order to accelerate the training convergence, a layer-based weight assignment scheme is designed, which decreases the amount of trainable weights. Simulation results show that the improved polar BP decoder with a one-bit quantizer outperforms the standard polar BP decoder with a 2-bit quantizer and achieves faster convergence.
Deep learning recently shows strong competitiveness to improve polar code decoding. However, suffering from prohibitive training and computation complexity, the conventional deep neural network (DNN) is only possible for very short code length. In this paper, the main problems of deep learning in decoding are well solved. We first present the multiple scaled belief propagation (BP) algorithm, aiming at obtaining faster convergence and better performance. Based on this, deep neural network decoder (NND) with low complexity and latency, is proposed for any code length. The training only requires a small set of zero codewords. Besides, its computation complexity is close to the original BP. Experiment results show that the proposed (64,32) NND with 5 iterations achieves even lower bit error rate (BER) than the 30-iteration conventional BP and (512, 256) NND also outperforms conventional BP decoder with same iterations. The hardware architecture of basic computation block is given and folding technique is also considered, saving about 50% hardware cost.
In recent years, neural network decoding of polar codes, such as neural belief propagation (BP), has been intro-duced. These methods use deep learning to transform the factor graph into a neural network model by unfolding the decoding iterations, thereby enhancing the accuracy of traditional decoding processes. However, current prevalent methodologies for loss function calculation only take into account the output of the final layer. In our analysis, we found that when calculating the loss function using only the output from the last layer, the convergence speed of the decoder significantly decreases, especially when the number of unfolded iterations is higher. In this paper, we incorporate the output of all iterations into the loss function in the original neural BP structure. Additionally, we optimize the loss function by assigning different weights to losses at different iterations. As a result, the weighted loss function not only provides a lower Bit Error Rate (BER) compared to the original neural BP decoder at lower SNR, but also accelerates convergence speed.
The polar neural decoder has a performance improvement at the cost of additional storage and computation. In this letter, we first propose a ResNet-like BP architecture to improve the standard polar BP decoding. Each iteration inherits a portion of information from the previous iteration as additional input and passes its output to the next iteration. Second, trainable damping factors, which can be learned through deep learning techniques, are applied to determine the inheritance ratio in the ResNet-like BP. We allocate the damping factors flexibly and demonstrate the optimization of a shared constant damping factor provides the same level of performance with the individual optimization of the damping factor at each state. Moreover, we qualitatively explain the performance gain by analyzing the mutual information between the input and output of the decoder. Numerical and simulation results indicate that the ResNet-like BP decoder can effectively improve the error correction performance and accelerate convergence compared with the standard polar BP algorithm.
In this paper, we present a sparse neural network decoder (SNND) of polar codes based on belief propagation (BP) and deep learning. At first, the conventional factor graph of polar BP decoding is converted to the bipartite Tanner graph similar to low-density parity-check (LDPC) codes. Then the Tanner graph is unfolded and translated into the graphical representation of deep neural network (DNN). The complex sum-product algorithm (SPA) is modified to min-sum (MS) approximation with low complexity. We dramatically reduce the number of weight by using single weight to parameterize the networks. Optimized by the training techniques of deep learning, proposed SNND achieves comparative decoding performance of SPA and obtains about 0.5 dB gain over MS decoding on (128,64) and (256,128) codes. Moreover, 60% complexity reduction is achieved and the decoding latency is significantly lower than the conventional polar BP.
A novel deep learning method for improving the belief propagation algorithm is proposed. The method generalizes the standard belief propagation algorithm by assigning weights to the edges of the Tanner graph. These edges are then trained using deep learning techniques. A well-known property of the belief propagation algorithm is the independence of the performance on the transmitted codeword. A crucial property of our new method is that our decoder preserved this property. Furthermore, this property allows us to learn only a single codeword instead of exponential number of codewords. Improvements over the belief propagation algorithm are demonstrated for various high density parity check codes.
In recent years, neural network-based BP decoders for polar codes have draw much attention, due to their faster convergence and better error-correction performance compared with conventional BP decoders. However, the prior neural BP decoders have high storage cost and training complexity due to massive number of training weights, and the performance improvement is slight. In this work, we first propose a 2D-MSMS algorithm with a shared weight scheme, in which the nodes in the same layer share a weight among different iterations. These learnable weights are optimized by deep learning techniques. Then, we propose a CRC-Aided relaxed 2D-MSMS polar de-coder by introducing relaxation method and CRC-Aided early termination scheme. Simulation results show that our proposed decoder can effectively improve BER performance at medium to high SNR and reduce the amount of training weights by more than 95%.