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International Conference on Communications

Multi-Label Neural Decoders for Block Codes

Cheuk Ting Leung, Rajshekhar Vishweshwar Bhat, Mehul Motani

Published Jun 1, 2020• 4 citations
Publisher

Abstract

The problem of decoding an (n, k, d) error-correcting block code, where a k-bit message word is mapped to an n-bit codeword, can be cast as a single-label classification problem. While it has been observed that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood decoder (MLD), the number of output nodes increases exponentially with k, making it prohibitive to implement for large k. To address this issue, we explore classification based multi-label neural decoders, in which the number of output nodes increases linearly with k. We consider well-known linear and non-linear block codes, as well as concatenated block codes, which have applications in emerging wireless networks. Our study finds that (i) although the number of output nodes linearly increases with k in a multi-label decoder, it requires more hidden layers and nodes in each hidden layer than the corresponding single-label decoder to achieve its best performance, and (ii) although one can design a multi-label decoder with bit error rate matching that of the MLD, it leaves more blocks in error leading to a reduced performance in terms of block error rate. We also note that the performance of the proposed decoder for concatenated codes is at least as good as that of a natural decoding algorithm in which the inner code is first decoded using the MLD and then the outer code is decoded with a polynomial-time decoding algorithm.

DOI
10.1109/icc40277.2020.9148786

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The problem of decoding an (n, k, d) error-correcting block code, where a k-bit message word is mapped to an n-bit codeword, can be cast as a single-label classification problem. While it has been observed that the performance of such single-label neural decoders closely approaches that of the corresponding maximum likelihood decoder (MLD), the number of output nodes increases exponentially with k, making it prohibitive to implement for large k. To address this issue, we explore classification based multi-label neural decoders, in which the number of output nodes increases linearly with k. We consider well-known linear and non-linear block codes, as well as concatenated block codes, which have applications in emerging wireless networks. Our study finds that (i) although the number of output nodes linearly increases with k in a multi-label decoder, it requires more hidden layers and nodes in each hidden layer than the corresponding single-label decoder to achieve its best performance, and (ii) although one can design a multi-label decoder with bit error rate matching that of the MLD, it leaves more blocks in error leading to a reduced performance in terms of block error rate. We also note that the performance of the proposed decoder for concatenated codes is at least as good as that of a natural decoding algorithm in which the inner code is first decoded using the MLD and then the outer code is decoded with a polynomial-time decoding algorithm.
We investigate the design of two neural network (NN) architectures recently proposed as decoders for forward error correction: the so-called single-label NN (SLNN) and multi-label NN (MLNN) decoders. These decoders have been reported to achieve near-optimal codeword- and bit-wise performance, respectively. Results in the literature show near-optimality for a variety of short codes. In this paper, we analytically prove that certain SLNN and MLNN architectures can, in fact, always realize optimal decoding, regardless of the code. These optimal architectures and their binary weights are shown to be defined by the codebook, i.e., no training or network optimization is required. Our proposed architectures are in fact not NNs, but implement the maximum likelihood decoding rule differently. Optimal performance is numerically demonstrated for Hamming (7; 4), Polar (16; 8), and BCH (31; 21) codes. The results show that our optimal architectures (which are not NNs) are less complex than the SLNN and MLNN architectures proposed in the literature, which in fact only achieve near-optimal performance. Extension to longer codes is still hindered by the curse of dimensionality. Therefore, even though SLNN and MLNN can perform maximum likelihood decoding, such architectures cannot be used for medium and long codes.
This paper analyzes the design and competitiveness of four neural network (NN) architectures recently proposed as decoders for forward error correction (FEC) codes. We first consider the so-called single-label neural network (SLNN) and the multi-label neural network (MLNN) decoders which have been reported to achieve near maximum likelihood (ML) performance. Here, we show analytically that SLNN and MLNN decoders can always achieve ML performance, regardless of the code dimensions-although at the cost of computational complexityand no training is in fact required. We then turn our attention to two transformer-based decoders: the error correction code transformer (ECCT) and the cross-attention message passing transformer (CrossMPT). We compare their performance against traditional decoders, and show that ordered statistics decoding outperforms these transformer-based decoders. The results in this paper cast serious doubts on the application of NN-based FEC decoders in the short and medium blocklength regime.
In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We improve on previous works in terms of allowing full decoding of the message rather than codewords, allowing thus the application to non-systematic codes, and proving that the single-message training property is still viable. The suggested system is implemented and tested on polar codes of sizes (64,32) and (128,64), and a BCH of size (63,51), leading to a significant improvement in both Bit Error Rate (BER) and Frame Error Rate (FER), with gains between 0.3dB and 1dB for the implemented codes in the high Signal-to-Noise Ratio (SNR) regime.
The problem of maximum likelihood decoding with a neural decoder for error-correcting code is considered. It is shown that the neural decoder can be improved with two novel loss terms on the node’s activations. The first loss term imposes a sparse constraint on the node’s activations. Whereas, the second loss term tried to mimic the node’s activations from a teacher decoder which has better performance. The proposed method has the same run time complexity and model size as the neural Belief Propagation decoder, while improving the decoding performance by up to1.1dB1.1dB1.1dBon BCH codes.
A very important and near optimum group of the block codes that have been developed in direction of Shannon's theory concept, is low density parity check (LDPC) code. There have been presented different algorithms for decoding of this class of code such as maximum likelihood (ML), bit flipping (BF), a posteriori probability (APP) and sum product (SP) algorithms that the first two of them decode by hard criterion and two others decode by soft criterion. In this article, considering LDPC codes structure and taking advantage of LDPC codes demonstrated by Tanner graph, we have presented a quite new method based on multi layer perceptron (MLP) neural networks that decodes LDPC codes by soft decision manner. This method opens another new way for LDPC and even other block codes decoding. Simulation results display good performance of this method compared to other known algorithms.
Polar codes using successive-cancellation decoding always suffer from high latency for its serial nature. Fast simplified successive-cancellation decoding algorithm improves the situation in theoretically but not performs well as expected in practical for the workload of nodes identification and the existence of many short blocks. Meanwhile, Neural network (NN) based decoders have appeared as potential candidates to replace conventional decoders for polar codes. But the exponentially increasing training complexity with information bits is unacceptable which means it is only suitable for short codes. In this paper, we present an improvement that increases decoding efficiency without degrading the error-correction performance. The long polar codes are divided into several sub-blocks, some of which can be decoded adopting fast maximum likelihood decoding method and the remained parts are replaced by several short codes NN decoders. The result shows that time steps the proposed algorithm need only equal to 79.8% of fast simplified successive-cancellation decoders require. Moreover, it has up to 21.2 times faster than successive-cancellation decoding algorithm. More importantly, the proposed algorithm decreases the hardness when applying in some degree.