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)

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

Geon Choi, Namyoon Lee

Published Dec 4, 2023• 5 citations
Publisher

Abstract

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.

DOI
10.1109/gcwkshps58843.2023.10464802

Related papers

Practical Decoding for Deep Polar Codes

Donghwa Han, Min Jang, Donghun Lee +2 more

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.

IEEE Globecom Workshops (GC Wkshps)•Dec 8, 2024•1 citation

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

Balanced Low-Complexity and Flexible Error-Correction List Flip Decoding for Polar Codes

Yansong Lv, Dai, Jingxin, Wang, Yuhuan +2 more

Benefiting from performance advantages under short code lengths, polar codes are well-suited for certain scenarios, such as the future Internet of Things (IoT) applications that require high reliability and low power. Existing list flip decoders can efficiently further enhance the error-correction performance of polar codes with finite code lengths, particularly the dynamic successive cancellation list flip (D-SCLF) decoder with flexible high-order error-correction capability (FHECC). However, to the best of our knowledge, current list flip decoders cannot effectively balance complexity and error-correction efficiency. To address this, we propose a parity-check-aided D-SCLF (PC-DSCLF) decoder. This decoder, based on FHECC and the characteristics of the list flip decoding process, introduces a simplified flip metric and a hybrid check scheme, along with a decoding method that supports the check scheme, enabling it to retain FHECC while achieving low complexity. Simulation results show that the proposed PC-DSCLF decoder achieves up to a 51.1\% average complexity reduction compared to the D-SCLF algorithm with distributed CRC for $PC(512, 256+24)$

arXiv:2303.12609•Mar 22, 2023•0 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

Block successive cancellation decoding of polarization-based codes

Dina Goldin, David Burshtein

Linear codes constructed using a polarization transformation followed by short blocklength sub-codes are proposed. Decoding is realized by the successive cancellation algorithm combined with standard optimal or non-optimal decoding of the sub-codes. List successive cancellation decoding can also be used. We demonstrate gains compared to standard successive cancellation of polar codes for short blocklength codes.

International Symposium on Turbo Codes and Iterative Information Processing•Sep 1, 2016•1 citation

Fast Node Polar Decoding Method Based on Hybrid Parity Check and CRC

Zongmiao He, Yangjun Chen, Shipeng Gao +3 more

In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.

IEEE Access•Jan 1, 2025•0 citations
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.
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.
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.
Benefiting from performance advantages under short code lengths, polar codes are well-suited for certain scenarios, such as the future Internet of Things (IoT) applications that require high reliability and low power. Existing list flip decoders can efficiently further enhance the error-correction performance of polar codes with finite code lengths, particularly the dynamic successive cancellation list flip (D-SCLF) decoder with flexible high-order error-correction capability (FHECC). However, to the best of our knowledge, current list flip decoders cannot effectively balance complexity and error-correction efficiency. To address this, we propose a parity-check-aided D-SCLF (PC-DSCLF) decoder. This decoder, based on FHECC and the characteristics of the list flip decoding process, introduces a simplified flip metric and a hybrid check scheme, along with a decoding method that supports the check scheme, enabling it to retain FHECC while achieving low complexity. Simulation results show that the proposed PC-DSCLF decoder achieves up to a 51.1\% average complexity reduction compared to the D-SCLF algorithm with distributed CRC for PC(512,256+24)PC(512, 256+24)PC(512,256+24)
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.
In the case of short code, polar code demonstrates superior performance compared with Low Density Parity Check (LDPC) code. Particularly in low coding rate scenario, the complexity of Polar code encoding and decoding is significantly lower than that of LDPC code. The technological advantage of Polar code makes it of great value in special application scenarios such as satellite communication and ocean communication. The polar coding scheme can significantly improve the transmission reliability of the communication system, because the satellite spread spectrum communication system generally adopts short code design.In the research of decoding algorithm, the original Serial Cancellation (SC) decoding algorithm has simple rules, but the decoding effect is not ideal under the limited code length, and the serial decoding mechanism leads to large decoding delay. The Successive Cancellation List (SCL) decoding algorithm improves decoding performance by increasing the number of decoding search path. However, maintaining multiple decoding paths can multiply the decoding complexity. Fast node-based decoding algorithm aims to accelerate decoding and reduce latency by defining and simplifying the decoding process for specific nodes, yet they do not optimize the decoding paths. In view of the above problems, this paper proposes a Simplified Parity Check-based Cyclic Redundancy Check (CRC)-Aided Successive Cancellation List (S-PC-CASCL) decoding algorithm. Simulation results demonstrate that the proposed S-PC-CASCL maintains excellent error correction performance while reducing the average list size by up to 16 % under low Signal Noise Ratio (SNR) conditions, thereby lowering computational complexity and decoding latency compared with other widely used polar decoding methods.