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

IEEE Globecom Workshops (GC Wkshps)

Practical Decoding for Deep Polar Codes

Donghwa Han, Min Jang, Donghun Lee, Seho Mlyung, Namyoon Lee

Published Dec 8, 2024• 1 citation
Publisher

Abstract

Pre-transformed polar codes constitute a broad class of codes constructed through the serial concatenation of outer codes and polar codes, enhancing the performance of standalone polar codes either by improving the weight distribution or by increasing the error-decay rate. Deep polar codes, a novel variant within this class, are constructed through a pre-transformation that involves a series of nested polar codes with increasing dimensions across layers. The proposed successive cancellation list with backpropagation parity check (SCL-BPC) decoder exploits the parity equations naturally arising from this nested encoding structure. In certain scenarios, deep polar codes with SCL-BPC decoding demonstrate superior performance compared to other pre-transformed polar codes. However, the SCL-BPC algorithm incurs additional decoding complexity and results in uneven decoding times. To address these issues, we investigate the matrix representation of the pre-transformation in deep polar codes and develop efficient implementation solutions for SCL-BPC decoding. Additionally, we introduce a low-complexity approach to SCL-BPC, which exhibits only a marginal reduction in performance.

DOI
10.1109/gcwkshp64532.2024.11100905

Related papers

Deep-Polar Codes: An Efficient Error Correction Code for Short Blocklength Transmission

Geon Choi, Namyoon Lee

In this paper, we put forth a novel class of pre-transformed polar codes, called as “deep-polar codes.” Encoding of deep-polar codes involves a series of multi-layered polar transformations. By applying these successive polar-based pre-transformations, deep-polar codes with an improved weight distribution are constructed with low encoding complexity. We also propose a low-complexity successive cancellation list decoding algorithm to effectively decode the deep-polar codes. This decoding algorithm harnesses the reverse process of the multi-layered pre-transformed encoding, referred to as “back propagation parity checks.” From simulations, we demonstrate that deep-polar codes outperform existing pre-transformed polar codes in terms of block error rates across various code rates and short blocklengths, while maintaining low-complexity encoding and decoding. Our findings highlight the effectiveness and practicality of deep-polar codes for short blocklength transmission scenarios in 6G.

IEEE Globecom Workshops (GC Wkshps)•Dec 4, 2023•5 citations

Fast List Decoding of High-Rate Polar Codes

Yang Lu, Minjian Zhao, Ming Lei +1 more

Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.

arXiv:2311.08188•IEEE Transactions on Communications•Jul 12, 2024•7 citations

Subcode Ensemble Decoding of Polar Codes

Henning Lulei, Jonathan Mandelbaum, Marvin Rübenacke +3 more

In the short block length regime, pre-transformed polar codes together with successive cancellation list (SCL) decoding possess excellent error correction capabilities. However, in practice, the list size is limited due to the suboptimal scaling of the required area in hardware implementations. Automorphism ensemble decoding (AED) can improve performance for a fixed list size by running multiple parallel SCL decodings on permuted received words, yielding a list of estimates from which the final estimate is selected. Yet, AED is limited to appropriately designed polar codes. Subcode ensemble decoding (ScED) was recently proposed for low-density parity-check codes and does not impose such design constraints. It uses multiple decodings in different subcodes, ensuring that the selected subcodes jointly cover the original code. We extend ScED to polar codes by expressing polar subcodes through suitable pre-transformations (PTs). To this end, we describe a framework classifying pre-transformations for pretransformed polar codes based on their role in encoding and decoding. Within this framework, we propose a new type of PT enabling ScED for polar codes, analyze its properties, and discuss how to construct an efficient ensemble.

arXiv:2504.17511•International Symposium on Turbo Codes and Iterative Information Processing•Aug 18, 2025•2 citations

Double-Parity-Check CA-SCL Encoding and Decoding for Polar Codes

Fang Yuan, Bin Tian

Due to the unsatisfactory block error rate (BLER) performance of short or moderate block , the further development of polar codes is limited. In this paper, the parity-check codes concatenated cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithms are studied. Then, an efficient concatenated method, double-parity-check CA-SCL (DP-CA-SCL) polar codes, is proposed according to exiting parity-check decoding algorithms. Not only can this new method improve the BLER performance in short or moderate block, but also it can guarantee the reduction of complexity relative to original CA-SCL method. The simulations in additive white Gaussian noise channel with binary phase shift keying modulation reveal that the DP-CA-SCL polar codes can provide significant performance gains. Comparing to the original CA-SCL decoding, there are 0.5 dB performance gains using proposed method at BLER of 10-3with (128, 64) polar codes. For another moderate block (256, 128) polar codes, it can also guarantee performance gains at least 0.18 dB.

International Conference on Signal Processing•Aug 1, 2018•5 citations

Deep-Learning-Aided Successive-Cancellation Decoding of Polar Codes

Seyyed Ali Hashemi, Nghia Doan, Thibaud Tonnellier +1 more

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.

arXiv:1912.01086•Asilomar Conference on Signals, Systems and Computers (ACSSC)•Nov 1, 2019•10 citations

Improved Logical Error Rate via List Decoding of Quantum Polar Codes

Anqi Gong, Joseph M. Renes

The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN log N) of SCL for code size$N$and list size L.

arXiv:2304.04743•IEEE International Symposium on Information Theory (ISIT)•Jul 7, 2024•1 citation
Pre-transformed polar codes constitute a broad class of codes constructed through the serial concatenation of outer codes and polar codes, enhancing the performance of standalone polar codes either by improving the weight distribution or by increasing the error-decay rate. Deep polar codes, a novel variant within this class, are constructed through a pre-transformation that involves a series of nested polar codes with increasing dimensions across layers. The proposed successive cancellation list with backpropagation parity check (SCL-BPC) decoder exploits the parity equations naturally arising from this nested encoding structure. In certain scenarios, deep polar codes with SCL-BPC decoding demonstrate superior performance compared to other pre-transformed polar codes. However, the SCL-BPC algorithm incurs additional decoding complexity and results in uneven decoding times. To address these issues, we investigate the matrix representation of the pre-transformation in deep polar codes and develop efficient implementation solutions for SCL-BPC decoding. Additionally, we introduce a low-complexity approach to SCL-BPC, which exhibits only a marginal reduction in performance.
In this paper, we put forth a novel class of pre-transformed polar codes, called as “deep-polar codes.” Encoding of deep-polar codes involves a series of multi-layered polar transformations. By applying these successive polar-based pre-transformations, deep-polar codes with an improved weight distribution are constructed with low encoding complexity. We also propose a low-complexity successive cancellation list decoding algorithm to effectively decode the deep-polar codes. This decoding algorithm harnesses the reverse process of the multi-layered pre-transformed encoding, referred to as “back propagation parity checks.” From simulations, we demonstrate that deep-polar codes outperform existing pre-transformed polar codes in terms of block error rates across various code rates and short blocklengths, while maintaining low-complexity encoding and decoding. Our findings highlight the effectiveness and practicality of deep-polar codes for short blocklength transmission scenarios in 6G.
Due to the ability to provide superior error-correction performance, the successive cancellation list (SCL) algorithm is widely regarded as one of the most promising decoding algorithms for polar codes with short-to-moderate code lengths. However, the application of SCL decoding in low-latency communication scenarios is limited due to its sequential nature. To reduce the decoding latency, developing tailored fast and efficient list decoding algorithms of specific polar constituent codes (special nodes) is a promising solution. Recently, fast list decoding algorithms are proposed by considering special nodes with low code rates. Aiming to further speedup the SCL decoding, this paper presents fast list decoding algorithms for two types of high-rate special nodes, namely single-parity-check (SPC) nodes and sequence rate one or single-parity-check (SR1/SPC) nodes. In particular, we develop two classes of fast list decoding algorithms for these nodes, where the first class uses a sequential decoding procedure to yield decoding latency that is linear with the list size, and the second further parallelizes the decoding process by pre-determining the redundant candidate paths offline. Simulation results show that the proposed list decoding algorithms are able to achieve up to 70.7% lower decoding latency than state-of-the-art fast SCL decoders, while exhibiting the same error-correction performance.
In the short block length regime, pre-transformed polar codes together with successive cancellation list (SCL) decoding possess excellent error correction capabilities. However, in practice, the list size is limited due to the suboptimal scaling of the required area in hardware implementations. Automorphism ensemble decoding (AED) can improve performance for a fixed list size by running multiple parallel SCL decodings on permuted received words, yielding a list of estimates from which the final estimate is selected. Yet, AED is limited to appropriately designed polar codes. Subcode ensemble decoding (ScED) was recently proposed for low-density parity-check codes and does not impose such design constraints. It uses multiple decodings in different subcodes, ensuring that the selected subcodes jointly cover the original code. We extend ScED to polar codes by expressing polar subcodes through suitable pre-transformations (PTs). To this end, we describe a framework classifying pre-transformations for pretransformed polar codes based on their role in encoding and decoding. Within this framework, we propose a new type of PT enabling ScED for polar codes, analyze its properties, and discuss how to construct an efficient ensemble.
Due to the unsatisfactory block error rate (BLER) performance of short or moderate block , the further development of polar codes is limited. In this paper, the parity-check codes concatenated cyclic redundancy check aided successive cancellation list (CA-SCL) decoding algorithms are studied. Then, an efficient concatenated method, double-parity-check CA-SCL (DP-CA-SCL) polar codes, is proposed according to exiting parity-check decoding algorithms. Not only can this new method improve the BLER performance in short or moderate block, but also it can guarantee the reduction of complexity relative to original CA-SCL method. The simulations in additive white Gaussian noise channel with binary phase shift keying modulation reveal that the DP-CA-SCL polar codes can provide significant performance gains. Comparing to the original CA-SCL decoding, there are 0.5 dB performance gains using proposed method at BLER of 10-3with (128, 64) polar codes. For another moderate block (256, 128) polar codes, it can also guarantee performance gains at least 0.18 dB.
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.
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN log N) of SCL for code sizeNNNand list size L.