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

Electronics Letters

Low‐latency BP decoder of polar code with alternate‐structure scheduling scheme

Xiaojun Zhang, Xiaofeng Yan, Jianming Cui, Yanfei Dong

Published Sep 4, 2020• 0 citations
Publisher

Abstract

In this Letter, a new scheduling scheme for belief propagation (BP) is proposed to reduce the decoding latency. All the stages update messages at the same time, it improves the reliability and accelerates the decoding convergence. The authors also remove the last stage of factor graph to reduce computational complexity. Simulations show that the average decoding latency of a (1024,512) polar code is reduced to 29.4 clocks.

DOI
10.1049/el.2020.1408

Related papers

Adaptive Reweighted Freezing Belief Propagation Decoding for Polar Codes

Xiaojin Guo, ZHANG Jingtao

To address the challenges of high computational redundancy, slow convergence speed, and limited decoding performance in Belief Propagation (BP) decoding of polar codes, this paper proposes an Adaptive Reweighted Freezing (ARF) BP decoding algorithm. This algorithm introduces an adaptive reweighting mechanism to regulate the weights of message updates, thereby accelerating the convergence of the decoding process. Furthermore, it implements a freezing judgment strategy for converged nodes within the factor graph to eliminate redundant calculations. Simulation results demonstrate that, in the low Signal-to-Noise Ratio (SNR) region, the ARF-BP algorithm achieves a performance gain of approximately 1.1 dB compared to the traditional BP decoding algorithm. Moreover, compared to BP decoding with the G-matrix early stopping criterion, it reduces the average number of iterations by about 64% and effectively freezes approximately 20% of the factor graph nodes. Featuring low latency and low power consumption, this algorithm is well-suited for critical scenarios such as 5G massive Machine Type Communications and Ultra-Reliable Low-Latency Communications.

•Jan 1, 2026•0 citations

Dual-Bit-Wise Stochastic Decoding for Polar Codes

Suwen Song, Lu Liu, Zhongfeng Wang +1 more

Polar codes, being the first class of codes with provable capacity-achieving property, have aroused extensive attention. The belief propagation (BP) algorithm, which is one of the popular decoding approaches for polar codes, possesses inherent high parallelism but also high computational complexity. With low complexity and high fault tolerance, stochastic computing has been well studied and applied to BP decoding for polar codes. However, existing stochastic BP decoders suffer from high decoding latency. In this paper, firstly, a novel dual-bit-wise iterative message update method is proposed for stochastic BP, reducing the decoding latency by more than half. Based on the dual-bit-wise decoding, more special nodes in the factor graph are investigated and then fully exploited to pursue lower decoding complexity than prior arts. Moreover, a well-optimized architecture is developed for the proposed stochastic decoder, where the random number generator (RNG), tracking forecast memory (TFM), and hard decision unit are intelligently designed for reduced hardware cost. Experimental results demonstrate that the presented decoder can exhibit 61.7% lower decoding latency than the state-of-the-art works. Besides, the throughput and hardware efficiency can be improved by nearly$2.8\times$and$2.7\times$, respectively.

IEEE Transactions on Signal Processing•Jan 1, 2023•3 citations

An Enhanced Belief Propagation Decoder for Polar Codes

Meng Zhang, Zhuo Li, Lijuan Xing

Belief propagation (BP) has attracted increasing attention due to its high parallelism. In this letter, a correction method is proposed to improve the block error rate (BLER) performance of the BP decoder for polar codes so that it is comparable to that of the successive cancellation list (SCL) decoder. Compared with BP flipping (BPF) decoding, the proposed decoder focuses on prior knowledge of the code bits in the factor graph. Two strategies have been proposed to construct the correction set. The simulation results show that the BPC decoder exhibits a BLER similar to that of BPF decoder while reducing the average latency and complexity by half. In addition, the BLER of the BPC decoder can approach that of the cyclic redundancy check (CRC)-aided SCL (CA-SCL) decoder in regions with low and medium signal-to-noise ratios (SNRs).

IEEE Communications Letters•Aug 11, 2021•16 citations

Enhancing Belief Propagation Decoding of Polar Codes: A Reinforcement Learning Approach

Mohsen Moradi, Salman Habib, David G. M. Mitchell

Short block-length polar-like codes showcase exceptional error correction performance (ECP) using sequential decoding or successive cancellation list decoding with a large list size. However, achieving a high level of reliability with these methods involves high-latency decoding. To meet the growing demand for low-latency communication with acceptable complexity, belief propagation (BP) decoding emerges as an attractive option, although its ECP is known to fall short of those high-latency alternatives. In this paper, we propose an enhanced BP decoding approach for polar codes, leveraging reinforcement learning (RL) to optimize the message-passing schedule. Moreover, we investigate the design of the polar code rate profile and corresponding Tanner graph representation to enhance the benefits of RL. Numerical results demonstrate a performance gain of more than 1 dB for polar codes with a length of 128 and a rate of 0.5 compared to conventional BP decoding alone at highEb/N0values, demonstrating the promise of the proposed approach.

IEEE Communications Letters•Apr 9, 2025•3 citations

Improved CRC aided BP decoding for polar codes

Sung‐Kwon Hong, Jong‐Moon Chung

Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.

Electronics Letters•Apr 22, 2021•3 citations

Improved LDPC-like BPL Decoding Algorithm for Polar Code

Rui Guo, Chenfei Zhang, Chen Lou

To improve the performance of BP decoding for polar codes, researchers have developed a Belief Propagation List (BPL) decoding algorithm by executing multiple BP decoders in parallel.This algorithm outperforms traditional BP decoding based on single graph decoding, although it sacrifices some complexity and delay.Unlike this basic Polar-BPL decoding mentioned above, a low-density parity check like (LDPC-like) BPL decoding algorithm has been introduced into polar codes.This algorithm performs more efficient BP decoding iterations on sparse graphs.To further reduce the complexity and delay of LDPC-like BPL, and avoid analyzing all sparse graphs, this article proposes an improved LDPC-like BPL (ILDPC-like BPL) decoding algorithm based on selecting factor graphs.This algorithm analyzes differences in permuted factor graphs and selects these graphs with non-convergent decoding results to form a decoding list, allowing decoding to be completed with fewer graphs traversed and iterations, thereby reducing complexity and delay.On this basis, to improve the reliability of this algorithm, this article further adds a path metric (PM) mechanism, which can dynamically evaluate different sparse graphs' results in parallel decoding.The simulation results show that compared with LDPC-like BPL (random scheme), ILDPC-like BPL improves decoding performance while reducing decoding delay and complexity; Compared with basic Polar-BPL (cycle-shift scheme), this algorithm greatly reduces decoding delay and complexity while achieving similar performance.

KSII Transactions on Internet and Information Systems•Jan 31, 2025•0 citations
In this Letter, a new scheduling scheme for belief propagation (BP) is proposed to reduce the decoding latency. All the stages update messages at the same time, it improves the reliability and accelerates the decoding convergence. The authors also remove the last stage of factor graph to reduce computational complexity. Simulations show that the average decoding latency of a (1024,512) polar code is reduced to 29.4 clocks.
To address the challenges of high computational redundancy, slow convergence speed, and limited decoding performance in Belief Propagation (BP) decoding of polar codes, this paper proposes an Adaptive Reweighted Freezing (ARF) BP decoding algorithm. This algorithm introduces an adaptive reweighting mechanism to regulate the weights of message updates, thereby accelerating the convergence of the decoding process. Furthermore, it implements a freezing judgment strategy for converged nodes within the factor graph to eliminate redundant calculations. Simulation results demonstrate that, in the low Signal-to-Noise Ratio (SNR) region, the ARF-BP algorithm achieves a performance gain of approximately 1.1 dB compared to the traditional BP decoding algorithm. Moreover, compared to BP decoding with the G-matrix early stopping criterion, it reduces the average number of iterations by about 64% and effectively freezes approximately 20% of the factor graph nodes. Featuring low latency and low power consumption, this algorithm is well-suited for critical scenarios such as 5G massive Machine Type Communications and Ultra-Reliable Low-Latency Communications.
Polar codes, being the first class of codes with provable capacity-achieving property, have aroused extensive attention. The belief propagation (BP) algorithm, which is one of the popular decoding approaches for polar codes, possesses inherent high parallelism but also high computational complexity. With low complexity and high fault tolerance, stochastic computing has been well studied and applied to BP decoding for polar codes. However, existing stochastic BP decoders suffer from high decoding latency. In this paper, firstly, a novel dual-bit-wise iterative message update method is proposed for stochastic BP, reducing the decoding latency by more than half. Based on the dual-bit-wise decoding, more special nodes in the factor graph are investigated and then fully exploited to pursue lower decoding complexity than prior arts. Moreover, a well-optimized architecture is developed for the proposed stochastic decoder, where the random number generator (RNG), tracking forecast memory (TFM), and hard decision unit are intelligently designed for reduced hardware cost. Experimental results demonstrate that the presented decoder can exhibit 61.7% lower decoding latency than the state-of-the-art works. Besides, the throughput and hardware efficiency can be improved by nearly2.8×2.8\times2.8×and2.7×2.7\times2.7×, respectively.
Belief propagation (BP) has attracted increasing attention due to its high parallelism. In this letter, a correction method is proposed to improve the block error rate (BLER) performance of the BP decoder for polar codes so that it is comparable to that of the successive cancellation list (SCL) decoder. Compared with BP flipping (BPF) decoding, the proposed decoder focuses on prior knowledge of the code bits in the factor graph. Two strategies have been proposed to construct the correction set. The simulation results show that the BPC decoder exhibits a BLER similar to that of BPF decoder while reducing the average latency and complexity by half. In addition, the BLER of the BPC decoder can approach that of the cyclic redundancy check (CRC)-aided SCL (CA-SCL) decoder in regions with low and medium signal-to-noise ratios (SNRs).
Short block-length polar-like codes showcase exceptional error correction performance (ECP) using sequential decoding or successive cancellation list decoding with a large list size. However, achieving a high level of reliability with these methods involves high-latency decoding. To meet the growing demand for low-latency communication with acceptable complexity, belief propagation (BP) decoding emerges as an attractive option, although its ECP is known to fall short of those high-latency alternatives. In this paper, we propose an enhanced BP decoding approach for polar codes, leveraging reinforcement learning (RL) to optimize the message-passing schedule. Moreover, we investigate the design of the polar code rate profile and corresponding Tanner graph representation to enhance the benefits of RL. Numerical results demonstrate a performance gain of more than 1 dB for polar codes with a length of 128 and a rate of 0.5 compared to conventional BP decoding alone at highEb/N0values, demonstrating the promise of the proposed approach.
Abstract In this letter, a modified message passing algorithm to prevent short cycles in the factor graph is proposed and combined with a relaxation technique to improve the performance of cyclic redundancy check aided belief propagation decoding for polar codes. Numerical results show that the proposed scheme can achieve a 0.7 dB coding gain, for the code rate of 0.5 at the block error rate of 10 −5 with a comparable average number of iterations over the pure belief propagation decoding scheme when the code block length is 1024.
To improve the performance of BP decoding for polar codes, researchers have developed a Belief Propagation List (BPL) decoding algorithm by executing multiple BP decoders in parallel.This algorithm outperforms traditional BP decoding based on single graph decoding, although it sacrifices some complexity and delay.Unlike this basic Polar-BPL decoding mentioned above, a low-density parity check like (LDPC-like) BPL decoding algorithm has been introduced into polar codes.This algorithm performs more efficient BP decoding iterations on sparse graphs.To further reduce the complexity and delay of LDPC-like BPL, and avoid analyzing all sparse graphs, this article proposes an improved LDPC-like BPL (ILDPC-like BPL) decoding algorithm based on selecting factor graphs.This algorithm analyzes differences in permuted factor graphs and selects these graphs with non-convergent decoding results to form a decoding list, allowing decoding to be completed with fewer graphs traversed and iterations, thereby reducing complexity and delay.On this basis, to improve the reliability of this algorithm, this article further adds a path metric (PM) mechanism, which can dynamically evaluate different sparse graphs' results in parallel decoding.The simulation results show that compared with LDPC-like BPL (random scheme), ILDPC-like BPL improves decoding performance while reducing decoding delay and complexity; Compared with basic Polar-BPL (cycle-shift scheme), this algorithm greatly reduces decoding delay and complexity while achieving similar performance.