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 Communications Letters

List-Based Residual Belief-Propagation Decoding of LDPC Codes

Ziqin Yan, Wu Guan, Liping Liang

Published Mar 25, 2024• 6 citations
Publisher

Abstract

This letter presents an enhanced list-based residual belief propagation (L-RBP) method for decoding low-density parity-check (LDPC) codes. L-RBP reduces computational complexity by scheduling a concise list of residuals. Moreover, the list is partially renewed to deter a small cluster of residuals from monopolizing renewal opportunities. Simultaneously, we also incorporate a decay mechanism to constrain the residuals retained within the list, further mitigating the greediness of the algorithm. The numerical results indicate that the L-RBP has an attractive convergence speed, error rate performance, and complexity of long-length and low-rate codes in the additive white Gaussian noise (AWGN) channel.

DOI
10.1109/lcomm.2024.3381220

Related papers

Residual-Decaying-Based Informed Dynamic Scheduling for Belief-Propagation Decoding of LDPC Codes

Huilian Zhang, Shaoping Chen

Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.

IEEE Access•Jan 1, 2019•19 citations

Reliability-List-Based Check-Belief Propagation Decoding of LDPC Codes

Zhe Liu, Wu Guan, Ziqin Yan +1 more

Reliability-based belief propagation (RBP) decoding algorithms are used to decode low-density parity-check (LDPC) codes. However, due to the reliability of comparing and sorting in traditional algorithms, conventional RBP decoders significantly lose in resource consumption. This letter presents an enhanced reliability list-based check-belief propagation (RL-CBP) algorithm. The RL-CBP algorithm reduces computational complexity by scheduling a concise list of check-beliefs. Moreover, the list is applied for comparisons and selections of check-beliefs. The selected check-belief transforms the decoding message between edges; all check-beliefs are iteratively enlarged according to the reliabilities, and high-performance decoding will be achieved. The simulation results and analyses show that the proposed method achieves a reliability-list gain compared with the check-belief propagation (CBP) algorithm but consumes much fewer calculations than the traditional RBP algorithm.

IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences•Dec 18, 2024•1 citation

Low-Latency LDPC Decoding Based on Consensus and Return Residual Belief Propagation

Allan E. Feitosa, Rodrigo C. de Lamare

We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER).

arXiv:2610.14387•Oct 9, 2026•0 citations

Consensus and Return Residual Belief Propagation for Low-Latency LDPC Decoding

Allan E. Feitosa, Rodrigo C. de Lamare

We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER). In particular, among all the algorithms considered, C&DR-RBP requires the fewest iterations to achieve a given error rate.

IEEE Access•Jan 1, 2026•0 citations

Informed dynamic schedules for LDPC decoding using belief propagation

Huang–Chang Lee, Yeong-Luh Ueng

After the publication of the residual belief-propagation (RBP) algorithm, many low-density parity-check (LDPC) decoders using informed dynamic scheduling (IDS) have been investigated. In this paper, we propose the twofold-RBP (T-RBP) decoder that combines two residuals. Using T-RBP, significant improvement can be achieved in both convergence speed and convergence error-rate performance. In addition to T-RBP, the simplified-RBP (S-RBP) decoder is also proposed in order to reduce the complexity. Instead of comparing all the residuals of all edges in the code graph, as with previous IDS decoders, S-RBP only compares the residuals of the edges connected to a single check node, thus dramatically reduces the complexity without any significant degradation in performance. The proposed T-RBP and S-RBP can improve not only the performance of dedicated codes, but also that of punctured codes, especially the convergence speed. The improvement can make punctured LDPC codes more practical and becoming a competitive candidate for the rate compatible applications.

IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)•Sep 1, 2013•4 citations

A Novel Fast LDPC Decoder Using APP-Based Dynamic Scheduling Scheme

Tian Xia, Hsiao‐Chun Wu, Scott C.-H. Huang

Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.

Globecom•Dec 1, 2015•3 citations
This letter presents an enhanced list-based residual belief propagation (L-RBP) method for decoding low-density parity-check (LDPC) codes. L-RBP reduces computational complexity by scheduling a concise list of residuals. Moreover, the list is partially renewed to deter a small cluster of residuals from monopolizing renewal opportunities. Simultaneously, we also incorporate a decay mechanism to constrain the residuals retained within the list, further mitigating the greediness of the algorithm. The numerical results indicate that the L-RBP has an attractive convergence speed, error rate performance, and complexity of long-length and low-rate codes in the additive white Gaussian noise (AWGN) channel.
Belief-propagation (BP) algorithm and its variants are well-established methods for iterative decoding of LDPC codes. Among them, residual belief-propagation (RBP), which is the most primitive and representative informed dynamic scheduling (IDS) strategy, can significantly accelerate the convergence speed. However, RBP decoding suffers from a poor convergence error-rate performance due to its greedy property, which is one of the challenging issues in the design of IDS strategies. To tackle this problem, a novel IDS scheme, namely residual-decaying-based residual belief-propagation (RD-RBP) algorithm, is presented in this paper. In RD-RBP, a decaying mechanism is introduced to manipulate the residuals of those check-to-variable messages, preventing the decoding resources from being unreasonably occupied by a small group of edges in the Tanner graph. The greediness is therefore alleviated and better performance of convergence error-rate is achieved. Besides, a two-stage scheduling scheme combining prior-art variable-node and variable-to-check-edge RBP (V-VCRBP) with RD-RBP, named V-VC-RD-RBP, is proposed for achieving both fast convergence speed and a low convergence error-rate. The simulation results validate the advantages of the proposed schemes.
Reliability-based belief propagation (RBP) decoding algorithms are used to decode low-density parity-check (LDPC) codes. However, due to the reliability of comparing and sorting in traditional algorithms, conventional RBP decoders significantly lose in resource consumption. This letter presents an enhanced reliability list-based check-belief propagation (RL-CBP) algorithm. The RL-CBP algorithm reduces computational complexity by scheduling a concise list of check-beliefs. Moreover, the list is applied for comparisons and selections of check-beliefs. The selected check-belief transforms the decoding message between edges; all check-beliefs are iteratively enlarged according to the reliabilities, and high-performance decoding will be achieved. The simulation results and analyses show that the proposed method achieves a reliability-list gain compared with the check-belief propagation (CBP) algorithm but consumes much fewer calculations than the traditional RBP algorithm.
We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER).
We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER). In particular, among all the algorithms considered, C&DR-RBP requires the fewest iterations to achieve a given error rate.
After the publication of the residual belief-propagation (RBP) algorithm, many low-density parity-check (LDPC) decoders using informed dynamic scheduling (IDS) have been investigated. In this paper, we propose the twofold-RBP (T-RBP) decoder that combines two residuals. Using T-RBP, significant improvement can be achieved in both convergence speed and convergence error-rate performance. In addition to T-RBP, the simplified-RBP (S-RBP) decoder is also proposed in order to reduce the complexity. Instead of comparing all the residuals of all edges in the code graph, as with previous IDS decoders, S-RBP only compares the residuals of the edges connected to a single check node, thus dramatically reduces the complexity without any significant degradation in performance. The proposed T-RBP and S-RBP can improve not only the performance of dedicated codes, but also that of punctured codes, especially the convergence speed. The improvement can make punctured LDPC codes more practical and becoming a competitive candidate for the rate compatible applications.
Low-density parity-check (LDPC) codes are favorable in modern telecommunication technologies due to its superior error-correction capability especially when the codeword length is large. The commonly-used LDPC decoders are based on the belief-propagation (BP) algorithms. It is well known that the layered (serial) belief-propagation (LBP) decoding algorithms can reduce the number of iterations by half in comparison with the flooding (parallel) BP decoding algorithms. Further reduction in total number of iterations can be achieved by using the informed dynamic scheduling techniques, such as residual BP (RBP) and node-wise residual BP (NWRBP) methods. However, the incurred additional computation of residuals is far from trivial. In this paper, we propose a novel efficient dynamic scheduling scheme, called a posteriori probability RBP (APPRBP) algorithm, which offers more flexibility to leverage the performance-complexity trade-off using a threshold parameter. The simulation results demonstrate that the average iteration numbers for our proposed APPRBP algorithm can be remarkably reduced especially in the low E_b/N_0 (signal-energy-per-information-bit to noise-power-spectral-density ratio) conditions while the bit-error rate (BER) performance is subject to slight degradation.