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arXiv:2604.17482

Node-Based Soft-Output Fast Successive Cancellation List Decoding of Polar Codes

Li Shen, Yongpeng Wu, Zhen Gao, Yin Xu, Xiaohu You, Xiqi Gao, Wenjun Zhang

Published Apr 19, 2026• 0 citations
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Abstract

The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder of polar codes. However, the sequential decoding nature of SCL introduces high decoding latency to SO-SCL. In this paper, we incorporate node-based fast decoding into the SO-SCL framework. After addressing the challenge of soft output extraction in special node decoding, we proposed the soft-output fast SCL (SO-FSCL) decoding algorithm, along with its log-domain implementation and hardware-friendly version. The proposed SO-FSCL decoder can be regarded as an add-on extension to FSCL decoder, enabling us to autonomously choose whether to output only hard decisions like FSCL or to provide additional soft outputs. Latency and complexity analyses demonstrate that SO-FSCL can significantly reduce, for example, decoding time steps by 81.8\% (with unlimited resources), the number of additions by 41.3\%, and the number of comparisons by 46.4\%. Meanwhile, simulation results indicate that SO-FSCL delivers almost the same soft-output performance as SO-SCL, outperforming other soft-output polar decoders, especially in scenarios involving iterative decoding.

DOI
10.48550/arxiv.2604.17482

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The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder of polar codes. However, the sequential decoding nature of SCL introduces high decoding latency to SO-SCL. In this paper, we incorporate node-based fast decoding into the SO-SCL framework. After addressing the challenge of soft output extraction in special node decoding, we proposed the soft-output fast SCL (SO-FSCL) decoding algorithm, along with its log-domain implementation and hardware-friendly version. The proposed SO-FSCL decoder can be regarded as an add-on extension to FSCL decoder, enabling us to autonomously choose whether to output only hard decisions like FSCL or to provide additional soft outputs. Latency and complexity analyses demonstrate that SO-FSCL can significantly reduce, for example, decoding time steps by 81.8% (with unlimited resources), the number of additions by 41.3%, and the number of comparisons by 46.4%. Meanwhile, simulation results indicate that SO-FSCL delivers almost the same soft-output performance as SO-SCL, outperforming other soft-output polar decoders, especially in scenarios involving iterative decoding.
The soft-output successive cancellation list (SOSCL) decoder provides a methodology for estimating the aposteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder of polar codes. However, the sequential decoding nature of SCL introduces high decoding latency to SOSCL. In this paper, we incorporate node-based fast decoding into the SO-SCL framework. After addressing the challenge of soft output extraction in special node decoding, we proposed the soft-output fast SCL (SO-FSCL) decoding algorithm, along with its log-domain implementation and hardware-friendly version. The proposed SO-FSCL decoder can be regarded as an addon extension to FSCL decoder, enabling us to autonomously choose whether to output only hard decisions like FSCL or to provide additional soft outputs. Latency and complexity analyses demonstrate that SO-FSCL can significantly reduce, for example, decoding time steps by 81.8% (with unlimited resources), the number of additions by 41.3%, and the number of comparisons by 46.4%. Meanwhile, simulation results indicate that SO-FSCL delivers almost the same soft-output performance as SO-SCL, outperforming other soft-output polar decoders, especially in scenarios involving iterative decoding.
The soft-output successive cancellation list (SO-SCL) decoder provides a methodology for estimating the a-posteriori probability log-likelihood ratios by only leveraging the conventional SCL decoder for polar codes. However, the sequential nature of SCL decoding leads to a high decoding latency for the SO-SCL decoder. In this paper, we propose a soft-output fast SCL (SO-FSCL) decoder by incorporating node-based fast decoding into the SO-SCL framework. Simulation results demonstrate that the proposed SO-FSCL decoder significantly reduces the decoding latency without loss of performance compared with the SO-SCL decoder.
Although the successive cancellation list (SCL) decoding of polar codes exhibits excellent performance, it retains many decoding paths in the list with negligible contribution to the final output, resulting in high sorting and computational complexity. In this letter, we propose a novel pruning strategy to mitigate the decoding complexity. By leveraging the blockwise soft output extraction process of soft-output SCL and soft-output fast SCL decoding, we provide an accurate approximation of the probability that a decoding path is correct, and thus accordingly prune the paths failing to meet a pre-defined reliability threshold. The complexity reduction achieved by the proposed soft-output-based pruned SCL (SOP-SCL) decoder and its fast version, SOP-FSCL decoder, is significant, without any compromise in error-correction performance. Meanwhile, they also prove to be more efficient than state-of-the-art pruned polar decoders.
Although the successive cancellation list (SCL) decoding of polar codes exhibits excellent performance, it retains many decoding paths in the list with negligible contribution to the final output, resulting in high sorting and computational complexity. In this letter, we propose a novel pruning strategy to mitigate the decoding complexity. By leveraging the blockwise soft output extraction process of soft-output SCL and soft-output fast SCL decoding, we provide an accurate approximation of the probability that a decoding path is correct, and thus accordingly prune the paths failing to meet a pre-defined reliability threshold. The complexity reduction achieved by the proposed soft-output-based pruned SCL (SOP-SCL) decoder and its fast version, SOP-FSCL decoder, is significant, without any compromise in error-correction performance. Meanwhile, they also prove to be more efficient than state-of-the-art pruned polar decoders.
The successive-cancellation list (SCL) and successive-cancellation flip (SCF) decoding can be used to improve the performance of polar codes, especially for short to moderate length codes. However, their serial decoding nature results in significant decoding latencies. Implementing some operations in parallel can reduce their decoding latencies. This paper presents fast implementations of the SCL and SCF decoders. In particular, we propose fast parallel list decoders for five newly identified types of nodes in the decoding tree of a polar code, which significantly improves the decoding latency. We also present novel fast SCF decoders that decode some special nodes in the decoding tree of a polar code without serially computing bit log-likelihood ratios. Using our proposed fast parallel SCF decoders, we observed an improvement up to 81% with respect to the original SCF decoder. This significant reduction in the decoding latency is observed without sacrificing the bit-error-rate performance of the code.
Compared with the bit-wise successive cancellation list (SCL) decoding of polar codes, the node-based Fast SCL decoding significantly reduces the decoding latency by identifying special constituent codes and decoding these in parallel. To further reduce the latency of current Fast SCL decoders, we first propose a fast sequence repetition (SR) node-based SCL (Fast SR-SCL) decoding algorithm, which only involves one type of node in the SCL decoding tree. Furthermore, we employ the adaptive path splitting (APS) strategy to terminate the path splitting in the SR node early, without degrading the error-correcting performance. Numerical results show that for 5G uplink codes with a length of 1024 and rates of 1/4, 1/2, and 3/4, our decoder can deliver the same decoding performance while reducing the average latency by 34.5%, 38.0%, and 39.6% compared with the state-of-the-art Fast SCL decoder for a list size L = 8.