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 International Conference on Software Engineering and Service Science (ICSESS)

A low-complexity LDPC belief propagation decoding in high order M-QAM modulation

Feng Hu, Siqi Liu, Libiao Jin, Ruofan Zhang

Published Nov 1, 2017• 1 citation
Publisher

Abstract

Belief propagation (BP) algorithm is commonly used in soft decoding of Low Density Parity Check Code (LDPC). However, a significant disadvantage of this method is that the computational complexity is high in high order M-QAM modulation. This paper proposes an optimized algorithm to reduce the posterior probability calculation in soft decoding, which estimates an approximate decision point in the constellation map via channel equalization. Then a contractible constellation decision space is delimited by the approximate decision point and its surrounding points with the minimum European distance. Compared with the conventional soft decoding, simulation results show that the proposed algorithm can effectively reduce the computational complexity of BP decoding with tiny loss of the decoding accuracy. The proposed algorithm reduces nearly 96 percent of the computational complexity of posterior probability in the case of 256QAM modulation.

DOI
10.1109/icsess.2017.8342951

Related papers

Check-Belief Propagation Decoding of LDPC Codes

Wu Guan, Liping Liang

Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.

arXiv:2305.05286•IEEE Transactions on Communications•Aug 24, 2023•16 citations

Quantum Approximate Optimization for Decoding of Low-Density Parity-Check Codes

Krishnakanta Barik, Goutam Paul

Decoding Low-Density Parity-Check (LDPC) codes is a fundamental problem in coding theory, and Belief Propagation (BP) is one of the most popular methods for LDPC code decoding. However, BP may encounter convergence issues and suboptimal performance, especially for short-length codes and in high-noise channels. The Quantum Approximate Optimization Algorithm (QAOA) is a type of Variational Quantum Algorithm (VQA) designed to solve combinatorial optimization problems by minimizing a problem-specific cost function. In this paper, we present a QAOA-based decoding framework for LDPC codes by formulating a decoding cost function that incorporates both parity-check constraints and soft channel reliability information. The resulting optimization problem is solved using QAOA to search for low-energy configurations corresponding to valid codewords. We test the proposed method through extensive numerical experiments and compare its performance with BP decoding. The experimental results demonstrate that the QAOA-based decoder achieves a higher probability of correctly recovering the transmitted codeword than BP across multiple experimental settings.

quant-pharXiv:2602.21124•IEEE International Conference on Quantum Control, Computing and Learning (qCCL)•Feb 25, 2026•0 citations

Simplified a Posteriori Probability Calculation for Binary LDPC Codes

Latifa Mostari, Abdelmalik Taleb Ahmed

The LDPC (Low-Density Parity-Check) decoder must operate soft decisions calculated using: LLR (Log-Likelihood Ratio) or APP (A Posteriori Probability) according to the decoding algorithm used. The exact calculation of these decisions for high order constellations involves complicated operations. In this work, a method to simplify the APP calculation is introduced. It is programmed to adapt as perfectly as possible the transmission system to the channel type in question. This method leads to simplify the implementation of the transmission system. Simulation results show that, under the Gaussian channel, the simplified APP algorithm for 16-QAM achieves the same performance that obtained with the exact APP, while for 64-QAM we have a small performance degradation. The same simplified APP algorithm that used for the Gaussian channel can be applied, with minor operations added, for Rayleigh channel, and it shows a small performance loss with respect to the exact APP.

•Oct 24, 2018•1 citation

A high‐performance belief propagation decoding algorithm for codes with short cycles

Ali Karimi-lenji, Monireh Houshmand, Fahimeh Zarmehi

Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.

International Journal of Communication Systems•Feb 28, 2017•2 citations

A Binary BP Decoding Using Posterior Adjustment for Quantum LDPC Codes

Tzu-Hsuan Huang, Yeong-Luh Ueng

Although belief propagation (BP) decoders are efficient and provide significant performance for classical low-density parity-check (LDPC) codes, they will suffer a degradation in performance for quantum LDPC (QLDPC) codes due to the limitations in the quantum field. In this paper, we propose a posterior adjustment of either a single qubit or multiple qubits within binary BP. The adjustment process changes the posterior likelihood ratio for one or multiple qubits according to the designed criterion. Simulations show the performance of both single and multi-qubit adjustment is able to outperform the conventional binary BP decoder and also outperform the BP decoder concatenated with the zero-order ordered-statistics decoding (BP+OSD-0). Moreover, with lower complexity, the performance when using our proposed decoder on the considered QLDPC codes can be close to high-order OSD.

IEEE International Conference on Acoustics Speech and Signal Processing•Mar 18, 2024•2 citations

Low-complexity Decoding Method of Generalized LDPC with Polar Component Codes

Wenxue Sun, Yin Xu, Hao Ju +5 more

Generalized low-density parity-check with polar component (GLDPC-PC) codes exhibit promising potential for 6G wireless systems with higher demands on reliability and data rate. The decoding method for GLDPC-PC codes involves belief propagation (BP), where the soft information of the component code is used as extrinsic information for check nodes. Although the Bahl-Cocke-Jelinek-Raviv (BCJR) decoding algorithm provides bitwise optimal soft information for linear block codes, its decoding complexity increases exponentially with the code length, making it impractical for applications. Therefore, the near-optimal soft-output successive cancellation list (SO-SCL) decoding with fixed scaling is proposed to reduce decoding complexity. However, the complexity of SO-SCL decoding still holds potential for further optimization. In this work, we propose an offline approximation of the unvisited probability codebook and a staged scaling strategy for the extrinsic information to reduce decoding complexity while maintaining low performance loss.

IEEE/CIC International Conference on Communications in China (ICCC)•Aug 10, 2025•0 citations
Belief propagation (BP) algorithm is commonly used in soft decoding of Low Density Parity Check Code (LDPC). However, a significant disadvantage of this method is that the computational complexity is high in high order M-QAM modulation. This paper proposes an optimized algorithm to reduce the posterior probability calculation in soft decoding, which estimates an approximate decision point in the constellation map via channel equalization. Then a contractible constellation decision space is delimited by the approximate decision point and its surrounding points with the minimum European distance. Compared with the conventional soft decoding, simulation results show that the proposed algorithm can effectively reduce the computational complexity of BP decoding with tiny loss of the decoding accuracy. The proposed algorithm reduces nearly 96 percent of the computational complexity of posterior probability in the case of 256QAM modulation.
Variant belief propagation (BP) algorithms are applied to low-density parity-check (LDPC) codes. However, conventional decoders suffer from a large resource consumption due to gathering messages from all the neighbour variable-nodes and/or check-nodes through cumulative calculations. In this paper, a check-belief propagation (CBP) decoding algorithm is proposed. Check-belief is used as the probability that the corresponding parity-check is satisfied. All check-beliefs are iteratively enlarged in a sequential recursive order, and successful decoding will be achieved after the check-beliefs are all big enough. Compared to previous algorithms employing a large number of cumulative calculations to gather all the neighbour messages, CBP decoding can renew each check-belief by propagating it from one check-node to another through only one variable-node, resulting in a low complexity decoding with no cumulative calculations. The simulation results and analyses show that the CBP algorithm provides little error-rate performance loss in contrast with the previous BP algorithms, but consumes much fewer calculations and memories than them. It earns a big benefit in terms of complexity.
Decoding Low-Density Parity-Check (LDPC) codes is a fundamental problem in coding theory, and Belief Propagation (BP) is one of the most popular methods for LDPC code decoding. However, BP may encounter convergence issues and suboptimal performance, especially for short-length codes and in high-noise channels. The Quantum Approximate Optimization Algorithm (QAOA) is a type of Variational Quantum Algorithm (VQA) designed to solve combinatorial optimization problems by minimizing a problem-specific cost function. In this paper, we present a QAOA-based decoding framework for LDPC codes by formulating a decoding cost function that incorporates both parity-check constraints and soft channel reliability information. The resulting optimization problem is solved using QAOA to search for low-energy configurations corresponding to valid codewords. We test the proposed method through extensive numerical experiments and compare its performance with BP decoding. The experimental results demonstrate that the QAOA-based decoder achieves a higher probability of correctly recovering the transmitted codeword than BP across multiple experimental settings.
The LDPC (Low-Density Parity-Check) decoder must operate soft decisions calculated using: LLR (Log-Likelihood Ratio) or APP (A Posteriori Probability) according to the decoding algorithm used. The exact calculation of these decisions for high order constellations involves complicated operations. In this work, a method to simplify the APP calculation is introduced. It is programmed to adapt as perfectly as possible the transmission system to the channel type in question. This method leads to simplify the implementation of the transmission system. Simulation results show that, under the Gaussian channel, the simplified APP algorithm for 16-QAM achieves the same performance that obtained with the exact APP, while for 64-QAM we have a small performance degradation. The same simplified APP algorithm that used for the Gaussian channel can be applied, with minor operations added, for Rayleigh channel, and it shows a small performance loss with respect to the exact APP.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
Although belief propagation (BP) decoders are efficient and provide significant performance for classical low-density parity-check (LDPC) codes, they will suffer a degradation in performance for quantum LDPC (QLDPC) codes due to the limitations in the quantum field. In this paper, we propose a posterior adjustment of either a single qubit or multiple qubits within binary BP. The adjustment process changes the posterior likelihood ratio for one or multiple qubits according to the designed criterion. Simulations show the performance of both single and multi-qubit adjustment is able to outperform the conventional binary BP decoder and also outperform the BP decoder concatenated with the zero-order ordered-statistics decoding (BP+OSD-0). Moreover, with lower complexity, the performance when using our proposed decoder on the considered QLDPC codes can be close to high-order OSD.
Generalized low-density parity-check with polar component (GLDPC-PC) codes exhibit promising potential for 6G wireless systems with higher demands on reliability and data rate. The decoding method for GLDPC-PC codes involves belief propagation (BP), where the soft information of the component code is used as extrinsic information for check nodes. Although the Bahl-Cocke-Jelinek-Raviv (BCJR) decoding algorithm provides bitwise optimal soft information for linear block codes, its decoding complexity increases exponentially with the code length, making it impractical for applications. Therefore, the near-optimal soft-output successive cancellation list (SO-SCL) decoding with fixed scaling is proposed to reduce decoding complexity. However, the complexity of SO-SCL decoding still holds potential for further optimization. In this work, we propose an offline approximation of the unvisited probability codebook and a staged scaling strategy for the extrinsic information to reduce decoding complexity while maintaining low performance loss.