Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Conference on Electronic Information Engineering and Computer Science (EIECS)

Multi-stack decoding Algorithm for Polarization-adjusted Convolutional Codes

Yuze Wu, Zhiliang Huang, Youyan Zhang, Shuihong Zhou

Published Sep 22, 2023• 1 citation
Publisher

Abstract

The Polar-Adjusted Convolutional (PAC) codes, improve the error correction ability of the polar code by concatenating convolutional transformation and polar transformation. For the traditional stack decoding algorithm, the ideal performance has not yet been achieved for some PAC codes. In this paper, we adopt a multi-stack decoding algorithm to further improve the error performance of PAC codes. In the multi-stack decoding algorithm, the original single stack is converted into multiple stacks, which expands the exploration path of decoding, obtains more possible decoding results, and improves the decoding performance of PAC codes. Compared to the single-stack decoding, the multi-stack decoding achieves a performance gain of approximately 0.2dB for a PAC code with code length 128 and rate 0.5.

DOI
10.1109/eiecs59936.2023.10435488

Related papers

Efficient Low-Memory Fast Stack Decoding with Variance Polarization for PAC Codes

Mohsen Moradi, Hessam Mahdavifar

Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node withN0leaf nodes in its corresponding subtree, conventional stack decoding must either explore all 2N0paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128, 64) code, our method achieves up to a 70% reduction in the average number of paths without degrading error-correction performance.

IEEE Open Journal of the Communications Society•Jan 1, 2026•0 citations

Bit-Flipping for Stack Decoding of Polarization-Adjusted Convolutional (PAC) Codes

Mohsen Moradi

While sequential decoding of polarization-adjusted convolutional (PAC) codes constructed using polar rate profile has low computational complexity, their error-correction per-formance falls far short of the theoretical bounds for finite blocklength codes. In this paper, we use the bit-flipping technique in the stack decoding algorithm of PAC codes in order to improve their error-correction performance. This technique maintains the low memory requirements of stack decoding and polar demapper. Additionally, at high SNR values, the number of visits at each level of the decoding tree is almost one. Numerical findings indicate that this approach is capable of outperforming the stack decoding algorithm.

International Workshop on Signal Design and its Applications in Communications•Aug 1, 2022•5 citations

Efficient Low-Memory Fast Stack Decoding with Variance Polarization for PAC Codes

Mohsen Moradi, Hessam Mahdavifar

Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with $N_0$ leaf nodes in its corresponding subtree, conventional stack decoding must either explore all $2^{N_0}$ paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC$(128,64)$ code, our method achieves up to a 70\% reduction in the average number of paths without degrading error-correction performance.

arXiv:2509.07231•Sep 8, 2025•0 citations

Fast List Decoding of PAC Codes With New Nodes

Jingxin Dai, Hang Yin, Yansong Lv +2 more

Polarization-adjusted convolutional (PAC) codes are special concatenated codes that utilize a one-to-one convolutional transform as a pre-coding step before the polar transform, thereby approaching the dispersion approximation for code (128, 64). However, current list decoders require an overly large list size to achieve near-bound performance, leading to unsatisfactory decoding latency. In this letter, we propose a fast list decoding algorithm with new special nodes for PAC codes, which effectively decreases decoding latency while preserving error-correction performance. Compared to the state-of-the-art work, the proposed algorithm can reduce decoding latency by up to 25.81% for the PAC code of length 128 with a code rate of 1/6.

IEEE Communications Letters•Jan 15, 2024•11 citations

Parity-Check Polarization-Adjusted Convolutional Coding

Qingping Yu, You ZHANG, Renze Luo +2 more

Polarization-adjusted convolutional (PAC) codes have better error-correcting performance than polar codes mostly because of the improved weight distribution brought by the convolutional pre-transformation. In this paper, we propose the parity check PAC (PC-PAC) codes to further improve error-correcting performance of PAC codes. The design principle is to establish parity check functions between bits with distinct row weights, such that information bits of lower reliability are re-protected by the PC relation. Moreover, an algorithm to select which bits to be involved in parity-check functions is also proposed to make sure that the constructed codes have fewer minimum-weight codewords. Simulation results show that the proposed PC-PAC codes can achieve nearly 0.2dB gain over PAC codes at frame error rate (FER) about 10-3 codes.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Jul 26, 2023•2 citations

Fast List Decoding of PAC Codes With Sequence Repetition Nodes

Ziwei Zhao, Minjian Zhao, Yang Lu +2 more

A latest coding scheme named polarization-adjusted convolutional (PAC) codes is shown to provide dramatic improvement in performance as compared to polar codes under list decoding. However, to achieve this performance gain, the list size needs to be excessively large, which may cause insufferable latency. For PAC codes, utilizing special nodes can reduce the time complexity. In this letter, we propose an extension of the sequence repetition (SR) nodes to PAC codes to further reduce the decoding latency. First, we define the notion of convolution-effected repetition sequences, which helps us to decode a specific SR node. Then, we propose a fast list decoding algorithm by taking the SR nodes into consideration. Simulation results indicate that the performance of the proposed decoding algorithm is almost identical to the original list decoding algorithm while achieving a higher degree of parallelism. In particular, for a PAC code of length 128 with code rate 1/4, the decoding latency can be reduced by over 35% as compared to the state-of-the-art fast list decoder.

IEEE Communications Letters•Aug 21, 2023•11 citations
The Polar-Adjusted Convolutional (PAC) codes, improve the error correction ability of the polar code by concatenating convolutional transformation and polar transformation. For the traditional stack decoding algorithm, the ideal performance has not yet been achieved for some PAC codes. In this paper, we adopt a multi-stack decoding algorithm to further improve the error performance of PAC codes. In the multi-stack decoding algorithm, the original single stack is converted into multiple stacks, which expands the exploration path of decoding, obtains more possible decoding results, and improves the decoding performance of PAC codes. Compared to the single-stack decoding, the multi-stack decoding achieves a performance gain of approximately 0.2dB for a PAC code with code length 128 and rate 0.5.
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node withN0leaf nodes in its corresponding subtree, conventional stack decoding must either explore all 2N0paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128, 64) code, our method achieves up to a 70% reduction in the average number of paths without degrading error-correction performance.
While sequential decoding of polarization-adjusted convolutional (PAC) codes constructed using polar rate profile has low computational complexity, their error-correction per-formance falls far short of the theoretical bounds for finite blocklength codes. In this paper, we use the bit-flipping technique in the stack decoding algorithm of PAC codes in order to improve their error-correction performance. This technique maintains the low memory requirements of stack decoding and polar demapper. Additionally, at high SNR values, the number of visits at each level of the decoding tree is almost one. Numerical findings indicate that this approach is capable of outperforming the stack decoding algorithm.
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced stack decoding algorithm for PAC codes that significantly improves parallelization by exploiting specialized bit nodes, such as rate-0 and rate-1 nodes. For a rate-1 node with N0N_0N0​ leaf nodes in its corresponding subtree, conventional stack decoding must either explore all 2N02^{N_0}2N0​ paths, or, same as in fast list decoding, restrict attention to a constant number of candidate paths. In contrast, our approach introduces a pruning technique that removes candidate paths with small path metrics while ensuring that the probability of pruning the correct path decays exponentially with the threshold. Furthermore, we propose a novel approximation method for estimating variance polarization under the binary-input additive white Gaussian noise (BI-AWGN) channel. Leveraging these approximations, we develop an efficient stack-pruning strategy that selectively preserves decoding paths whose bit-metric values align with their expected means. This targeted pruning substantially reduces the number of active paths in the stack, thereby decreasing both decoding latency and computational complexity. Numerical results demonstrate that for a PAC(128,64)(128,64)(128,64) code, our method achieves up to a 70\% reduction in the average number of paths without degrading error-correction performance.
Polarization-adjusted convolutional (PAC) codes are special concatenated codes that utilize a one-to-one convolutional transform as a pre-coding step before the polar transform, thereby approaching the dispersion approximation for code (128, 64). However, current list decoders require an overly large list size to achieve near-bound performance, leading to unsatisfactory decoding latency. In this letter, we propose a fast list decoding algorithm with new special nodes for PAC codes, which effectively decreases decoding latency while preserving error-correction performance. Compared to the state-of-the-art work, the proposed algorithm can reduce decoding latency by up to 25.81% for the PAC code of length 128 with a code rate of 1/6.
Polarization-adjusted convolutional (PAC) codes have better error-correcting performance than polar codes mostly because of the improved weight distribution brought by the convolutional pre-transformation. In this paper, we propose the parity check PAC (PC-PAC) codes to further improve error-correcting performance of PAC codes. The design principle is to establish parity check functions between bits with distinct row weights, such that information bits of lower reliability are re-protected by the PC relation. Moreover, an algorithm to select which bits to be involved in parity-check functions is also proposed to make sure that the constructed codes have fewer minimum-weight codewords. Simulation results show that the proposed PC-PAC codes can achieve nearly 0.2dB gain over PAC codes at frame error rate (FER) about 10-3 codes.
A latest coding scheme named polarization-adjusted convolutional (PAC) codes is shown to provide dramatic improvement in performance as compared to polar codes under list decoding. However, to achieve this performance gain, the list size needs to be excessively large, which may cause insufferable latency. For PAC codes, utilizing special nodes can reduce the time complexity. In this letter, we propose an extension of the sequence repetition (SR) nodes to PAC codes to further reduce the decoding latency. First, we define the notion of convolution-effected repetition sequences, which helps us to decode a specific SR node. Then, we propose a fast list decoding algorithm by taking the SR nodes into consideration. Simulation results indicate that the performance of the proposed decoding algorithm is almost identical to the original list decoding algorithm while achieving a higher degree of parallelism. In particular, for a PAC code of length 128 with code rate 1/4, the decoding latency can be reduced by over 35% as compared to the state-of-the-art fast list decoder.