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International Conference on Wireless Communications and Signal Processing (WCSP)

A Graph-Neural-Network Decoder with MLP-based Processing Cells for Polar Codes

Xuran Song, Zhaoyang Zhang, Jue Wang, Kangjian Qin

Published Oct 1, 2019• 3 citations
Publisher

Abstract

Compared with traditional decoders, the Neural Network Decoder (NND)has the advantages of being low-latency, high-throughput and one-shot. However, the conventional deep neural network decoder (DNND)usually suffers the computational mismatch and the lack of generalization capability. In this paper, we propose a novel Graph-Neural-Network Decoder for the popular Polar Codes, which is directly constructed based on the regular decoding graph of Polar Codes and by replacing each of its basic 2-by-2 polarization elements with a simple Multi-Layer-Perceptron (MLP)based processing cell. The resultant decoder, namely PC-GNND, is thus endowed with the ability to infer over the skeleton of the decoding graph and has a greatly improved generalization capability. Simulation results show that, the proposed PC-GNND is capable of learning the exact code structure as well as the channel noise very efficiently with only a tiny fraction of the entire codebook and achieving better performance than that of conventional NNDs with far less parameters and training epochs. Moreover, the PC-GNND trained in a particular block length can be scaled to another one for different block lengths after fine tuning, which significantly reduces the computational cost of training.

DOI
10.1109/wcsp.2019.8928139

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Compared with traditional decoders, the Neural Network Decoder (NND)has the advantages of being low-latency, high-throughput and one-shot. However, the conventional deep neural network decoder (DNND)usually suffers the computational mismatch and the lack of generalization capability. In this paper, we propose a novel Graph-Neural-Network Decoder for the popular Polar Codes, which is directly constructed based on the regular decoding graph of Polar Codes and by replacing each of its basic 2-by-2 polarization elements with a simple Multi-Layer-Perceptron (MLP)based processing cell. The resultant decoder, namely PC-GNND, is thus endowed with the ability to infer over the skeleton of the decoding graph and has a greatly improved generalization capability. Simulation results show that, the proposed PC-GNND is capable of learning the exact code structure as well as the channel noise very efficiently with only a tiny fraction of the entire codebook and achieving better performance than that of conventional NNDs with far less parameters and training epochs. Moreover, the PC-GNND trained in a particular block length can be scaled to another one for different block lengths after fine tuning, which significantly reduces the computational cost of training.
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.
We propose a self-supervised deep learning-based decoding scheme that enables one-shot decoding of polar codes. In the proposed scheme, rather than using the information bit vectors as labels for training the neural network (NN) through supervised learning as the conventional scheme did, the NN is trained to function as a bounded distance decoder by leveraging the generator matrix of polar codes through self-supervised learning. This approach eliminates the reliance on predefined labels, empowering the potential to train directly on the actual data within communication systems and thereby enhancing the applicability. Furthermore, computer simulations demonstrate that (i) the bit error rate (BER) and block error rate (BLER) performances of the proposed scheme can approach those of the maximum a posteriori (MAP) decoder for very short packets and (ii) the proposed NN decoder (NND) exhibits much superior generalization ability compared to the conventional one.
The training complexity of deep learning-based channel decoders scales exponentially with the codebook size and therefore with the number of information bits. Thus, neural network decoding (NND) is currently only feasible for very short block lengths. In this work, we show that the conventional iterative decoding algorithm for polar codes can be enhanced when sub-blocks of the decoder are replaced by neural network (NN) based components. Thus, we partition the encoding graph into smaller sub-blocks and train them individually, closely approaching maximum a posteriori (MAP) performance per sub-block. These blocks are then connected via the remaining conventional belief propagation decoding stage(s). The resulting decoding algorithm is non-iterative and inherently enables a highlevel of parallelization, while showing a competitive bit error rate (BER) performance. We examine the degradation through partitioning and compare the resulting decoder to state-of-the art polar decoders such as successive cancellation list and belief propagation decoding.
In this work, we propose a fully differentiable graph neural network (GNN)-based architecture for channel decoding and showcase a competitive decoding performance for various coding schemes, such as low-density parity-check (LDPC) and BCH codes. The idea is to let a neural network (NN) learn a generalized message passing algorithm over a given graph that represents the forward error correction (FEC) code structure by replacing node and edge message updates with trainable functions. Contrary to many other deep learning-based decoding approaches, the proposed solution enjoys scalability to arbitrary block lengths and the training is not limited by the curse of dimensionality. We benchmark our proposed decoder against state-of-the-art in conventional channel decoding as well as against recent deep learning-based results. For the (63,45) BCH code, our solution outperforms weighted belief propagation (BP) decoding by approximately 0.4 dB with significantly less decoding iterations and even for 5G NR LDPC codes, we observe a competitive performance when compared to conventional BP decoding. For the BCH codes, the resulting GNN decoder can be fully parametrized with only 9640 weights.
Compared with binary Polar codes, non-binary Polar codes exhibit better performance, which is suitable for short packet services of Internet of Things. But its decoding complexity is high(O(2Nlog⁡2(N))(O(2N\log_{2}(N))(O(2Nlog2​(N)), whereNNNis the length of the symbol sequence). To make it practical, this paper proposes a sparse neural network (SNN) decoder. Firstly, the Polar factor graph is transformed into a bipartite graph which contains variable node and check node. Then, we propose a pruning algorithm to prune the bipartite graph so as to get a sparse graph. After that, the sparse graph is expanded to get the structure of the deep neural network. Optimized by the training of deep learning, the proposed SNN decoding scheme has competitive performance to the traditional Belief-Propagation (BP) decoding scheme. Moreover, the SNN decoder achieves a reduction of 51.7% in the number of connections compared with BP decoding scheme and its decoding latency is significantly lower than the traditional BP.
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.