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arXiv:2605.23124 · IEEE Transactions on Cognitive Communications and Networking

Deep-Learning-Aided Successive Cancellation List Flip Decoding for Polar Codes

Fu-Siang Liang, Shan Lu, Yeong-Luh Ueng

Published Oct 20, 2023• 5 citations
arXivHTMLPDF

Abstract

Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next decoding attempt. To identify the erroneous bits, the Log-Likelihood Ratio (LLR) is used to indicate the reliability of each decision bit. To improve the accuracy of the erroneous bit prediction, we propose deep-learning-aided (DL-aided) SCLF decoding algorithms. We first offer a stacked LSTM network that contains new features to train our models, which are able to improve the accuracy of the prediction of positions of erroneous bits. Then we separately train the stacked LSTM models to predict the position of both the first and second erroneous bits and whether to continue flipping. As a result, the DL-aided SCLF decoding algorithms based on the proposed stacked LSTM flip-1 model, stacked LSTM flip-2 model, and the stacked LSTM continue-flipping check (CFC) model are able to provide a better performance at a lower number of average decoding attempts when compared to other state-of-the-art decoding algorithms.

DOI
10.1109/tccn.2023.3326330

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Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next decoding attempt. To identify the erroneous bits, the Log-Likelihood Ratio (LLR) is used to indicate the reliability of each decision bit. To improve the accuracy of the erroneous bit prediction, we propose deep-learning-aided (DL-aided) SCLF decoding algorithms. We first offer a stacked LSTM network that contains new features to train our models, which are able to improve the accuracy of the prediction of positions of erroneous bits. Then we separately train the stacked LSTM models to predict the position of both the first and second erroneous bits and whether to continue flipping. As a result, the DL-aided SCLF decoding algorithms based on the proposed stacked LSTM flip-1 model, stacked LSTM flip-2 model, and the stacked LSTM continue-flipping check (CFC) model are able to provide a better performance at a lower number of average decoding attempts when compared to other state-of-the-art decoding algorithms.
The key to successive cancellation (SC) flip decoding of polar codes is to accurately identify the first error bit. The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, we propose a deep learning aided SC flip algorithm. Specifically, before each SC decoding attempt, a long short-term memory (LSTM) network is exploited to either (i) locate the first error bit, or (ii) undo a previous "wrong" flip. In each SC attempt, the sequence of log likelihood ratios (LLRs) derived in the previous SC attempt is exploited to decide which action to take. Accordingly, a two-stage training method of the LSTM network is proposed, i.e., learn to locate first error bits in the first stage, and then to undo "wrong" flips in the second stage. Simulation results show that the proposed approach identifies error bits more accurately and achieves better block error rate performance than the state-of-the-art SC flip algorithms.
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive cancellation list bit-flipping (CA-SCLF) decoders have been developed to obtain a better performance, the solution to error bit correction (bit-flipping) problem is still imperfect and hard to design. In this work, we leverage the expert knowledge in communication systems and adopt deep learning (DL) technique to obtain the better solution. A low-complexity long short-term memory network (LSTM)-assisted CA-SCLF decoder is proposed to further improve the performance of conventional CA-SCLF and avoid complexity and memory overhead. Our test results show that we can effectively improve the BLER performance by 0.11dB compared to prior work and reduce the complexity and memory overhead by over 30% of the network.
A deep-learning-aided successive-cancellation list (DL-SCL) decoding algorithm for polar codes is introduced with deep-learning-aided successive-cancellation (DL-SC) decoding being a specific case of it. The DL-SCL decoder works by allowing additional rounds of SCL decoding when the first SCL decoding attempt fails, using a novel bit-flipping metric. The proposed bit-flipping metric exploits the inherent relations between the information bits in polar codes that are represented by a correlation matrix. The correlation matrix is then optimized using emerging deep-learning techniques. Performance results on a polar code of length 128 with 64 information bits concatenated with a 24-bit cyclic redundancy check show that the proposed bit-flipping metric in the proposed DL-SCL decoder requires up to 66% fewer multiplications and up to 36% fewer additions, without any need to perform transcendental functions, and by providing almost the same error-correction performance in comparison with the state of the art.
Polar codes have attracted much attention in the past decade due to their capacity-achieving performance. The higher decoding capacity is required for 5G and beyond 5G (B5G). Although the cyclic redundancy check (CRC)- assisted successive cancellation list bit-flipping (CA-SCLF) decoders have been developed to obtain a better performance, the solution to error bit correction (bitflipping) problem is still imperfect and hard to design. In this work, we leverage expert knowledge in communication systems and adopt deep learning (DL) techniques to obtain a better solution. A low-complexity long short-term memory network (LSTM)-assisted CASCLF decoder is proposed to further improve the performance of conventional CA-SCLF and avoid complexity and memory overhead. Our test results show that we can effectively improve the BLER performance by 0.11dB compared to prior work and reduce the complexity and memory overhead by over 30% of the network.
Recently, the dynamic-successive cancellation list flip (D-SCLF) decoder has been proposed to improve the high-order flipping performance of existing successive cancellation list flip (SCLF) decoders in polar codes decoding. However, the D-SCLF decoder involves a large number of exponential and logarithmic operations, resulting in an exponential increase in computational complexity. To further improve the performance and reduce the average complexity of D-SCLF decoding, the deep learning-assisted adaptive dynamic-SCLF (DL-AD-SCLF) decoding is proposed in this paper. The error metric of D-SCLF decoding is re-derived, and an approximation scheme is proposed to reduce computational complexity. To compensate the loss of performance due to approximation, two learnable parameters are introduced. Customized neural network structures are proposed to optimize these learnable parameters according to the improved error metric by employing deep learning (DL), and the deep learning-assisted dynamic-SCLF (DL-D-SCLF) decoding is proposed. Furthermore, the adaptive list is introduced into the DL-D-SCLF decoding to further reduce decoding complexity. Simulation results show that the proposed decoder performance is improved up to 0.35dB and 0.25dB, the average complexity is reduced by up to 57.65% and 51.48% for single-bit and multi-bit flipping, respectively. Additionally, the proposed decoder exhibits good robustness to changes in code rates, code lengths, and channel conditions.
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.