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International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY)

Method of Critical Set construction for Successive Cancellation List Decoder of Polar Codes Based on Deep Learning of Neural Networks

Feodosii Kotov, Fedor I. Ivanov, Ilya Timokhin

Published Oct 24, 2023• 1 citation
Publisher

Abstract

The Successive Cancellation List (SCL) algorithm is a widely used decoding technique in communication systems. However, constructing the critical set for SCL decoding is a challenging task, as it requires a large number of computations and can lead to significant decoding delays. In this paper, a new approach to critical set construction for SCL decoding is proposed, which is based on deep learning of neural networks with special structure and activation functions.The proposed method is shown to significantly reduce the cardinality of the critical set required for achieving the target frame error rate, when used with an SCL decoder with a list size of 8. Simulation results demonstrate that the proposed method outperforms existing methods in terms of reducing decoding delay, while maintaining high decoding accuracy.The key innovation of the proposed approach lies in the use of deep learning techniques to learn the structure of the critical set, which enables the construction of a more efficient and compact set. This approach has the potential to significantly improve the performance of SCL decoding in practical communication systems, where decoding delay is a critical factor.

DOI
10.1109/redundancy59964.2023.10330189

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The Successive Cancellation List (SCL) algorithm is a widely used decoding technique in communication systems. However, constructing the critical set for SCL decoding is a challenging task, as it requires a large number of computations and can lead to significant decoding delays. In this paper, a new approach to critical set construction for SCL decoding is proposed, which is based on deep learning of neural networks with special structure and activation functions.The proposed method is shown to significantly reduce the cardinality of the critical set required for achieving the target frame error rate, when used with an SCL decoder with a list size of 8. Simulation results demonstrate that the proposed method outperforms existing methods in terms of reducing decoding delay, while maintaining high decoding accuracy.The key innovation of the proposed approach lies in the use of deep learning techniques to learn the structure of the critical set, which enables the construction of a more efficient and compact set. This approach has the potential to significantly improve the performance of SCL decoding in practical communication systems, where decoding delay is a critical factor.
Existing studies have documented that flipping operation can improve the performance of polar codes based on CRC-aided successive cancellation list (CA-SCL) decoding algorithm. However, the introduction of the flips greatly increases the complexity and delay of the decoder as well. In this paper, we analyzed the error distribution in the CA-SCL decoding and proposed a new efficient flipping set, key set, to reduce the complexity of the SCL-Flip decoding by narrowing down the size of the flipping set applicable. Different from the critical set which focuses on rate-1 nodes only, the key set can be constructed dynamically based on the results of the original CA-SCL decoding. In addition, we proposed an order-1 SCL-Flip decoder based on the key set to reduce the decoding complexity. Simulation results showed that the key set has a high accuracy of locating the first error and our proposed algorithm has almost no performance degradation compared with the existing SCL-Flip algorithms while the average complexity is reduced significantly.
Recently, a generalized successive cancellation list (SCL) decoder implemented with shifted-pruning (SP) scheme, namely the SCL-SP-ω decoder, is presented for polar codes, which is able to shift the pruning window at most ω times during each SCL re-decoding attempt to prevent the correct path from being eliminated. The candidate positions for applying the SP scheme are selected by a shifting metric based on the probability that the elimination occurs. However, the number of exponential/logarithm operations involved in the SCL-SP-ω decoder grows linearly with the number of information bits and list size, which leads to high computational complexity. In this paper, we present a detailed analysis of the SCL-SP-ω decoder in terms of the decoding performance and complexity, which unveils that the choice of the shifting metric is essential for improving the decoding performance and reducing the re-decoding attempts simultaneously. Then, we introduce a simplified metric derived from the path metric (PM) domain, and a custom-tailored deep learning (DL) network is further designed to enhance the efficiency of the proposed simplified metric. The proposed metrics are both free of transcendental functions and hence, are more hardware-friendly than the existing metrics. Simulation results show that the proposed DL-aided metric provides the best error correction performance as comparison with the state of the art.
Combined with cyclic redundancy check (CRC), SC list (SCL) decoder can achieve outstanding error correction performance, which is more obvious with increasing list size. However, the corresponding decoding complexity and latency increase with the list size. To this end, the selection of list size becomes essential for practical applications. A new artificial neural network (ANN) based framework is proposed in this paper to design a hardware-friendly adaptive SCL (DL-ASCL) decoder. First, the list size at each stage is predicted by an ANN predictor. The performance achieved based on the proposed DL-ASCL algorithm is close to the optimal SCL decoder with the same list size, especially in the high signal-to-noise ratio (SNR) region. Meanwhile, the computational complexity is significantly reduced compared with the conventional ones. Numerical results have demonstrated that the proposed deep learning based adaptive SCL decoder can achieve 56% computational complexity reduction compared with the conventional SCL decoder for the polar code with length 128 and rate 1/2. The hardware architecture of the adaptive SCL decoder based on the predicted list size is proposed and the folding technique is also adopted, which helps reduce the hardware cost by about 25%.
We investigate the cyclic redundancy check (CRC) codes aided successive cancellation list (SCL) decoding schemes to improve the performance of Polar codes. Distinguished from the existing literatures of Polar codes that only consider the error detection capability of CRC, we attempt to take advantage of the inherent error correction capability of CRC and we first devise a segmented CRC-error-correcting aided SCL decoding (SCC-SCL) framework. Based on this framework, an error-correcting table based SCC-SCL (ET-SCC-SCL) decoding scheme is proposed, by introducing the look-up-table based CRC error correction method into the segmented Polar SCL decoding process. Since the error correction capability is limited by the size of the look-up table, which in turn limits the performance gain, we further propose a deep learning based SCC-SCL (DL-SCC-SCL) decoding scheme. In this scheme, a long short-term memory (LSTM) network replaces the error correction table to perform error correction, combining the sequence of log likelihood ratios (LLRs) with the syndromes to determine the error patterns. Simulation results show that both of the proposed decoding schemes have significant performance gain over the classic CRC error-detection aided SCL decoding scheme. Especially for the DL-SCC-SCL, the performance gain at bit error rate of 10-5is about 0.5 dB.
Successive cancellation list (SCL) decoder has high decoding performance but also require great resource consumption. In this paper, we combine the SCL decoder and the critical set to form a new decoder, which can stably reduce the number of operations by 65%$\sim$70% and maintain similar decoding performance to SCL decoder. The reduction in resource consumption depends only on the arrangement of unfrozen bit sequences, not on the quality of the channel. We also propose to combine this new decoder with adaptive algorithms. In this way, the decoding performance of the decoder can be improved beyond SCL decoders without increasing resource consumption.
Successive-cancellation list (SCL) decoding of polar codes has been adopted for 5G wireless communications. How-ever, the performance of moderate code length is not satisfactory. Heuristic or deep-learning-aided (DL-aided) flip algorithms have been developed to improve the performance by locating error bit positions after SCL decoding. In this work, we propose a new flip algorithm with the help of differentiable neural computer (DNC). New state and action encoding are developed to improve DNC training and inference efficiency. The proposed two-phase method is done by a flip DNC (F-DNC) to rank the most likely flip positions for multi-bit flipping, and if decoding still fails, a flip-validate DNC (FV-DNC) is applied to re-select error bit positions in successive flip decoding trials. Supervised training methods are designed for the two DNCs. Simulation results show that the proposed DNC-aided SCL-Flip (DNC-SCLF) decoding demonstrates up to 0.34 dB coding gain or 54.2% reduction in the average number of decoding attempts over prior work.